Loop-and-allied QG bibliography

[kodama]

MOND as a regime of quantum gravity
Lee Smolin
(Submitted on 3 Apr 2017)
We propose that there is a regime of quantum gravity phenomena, for the case that the cosmological constant is small and positive, which concerns phenomena at temperatures below the deSitter temperature, or length scales larger than the horizon. We observe that the standard form of the equivalence principle does not apply in this regime; we consider instead that a weakened form of the equivalence principle might hold in which the ratio of gravitational to inertial mass is a function of environmental and global parameters. We consider possible principles to determine that function. These lead to behaviour that, in the limit of hbar to zero and the speed of light is taken to infinity, reproduces the modifications of Newtonian dynamics first proposed by Milgrom. Thus MOND is elucidated as coding the physics of a novel regime of quantum gravity phenomena.
We propose also an effective description of this regime in terms of a bi-metric theory, valid in the approximation where the metric is static. This predicts a new effect, which modifies gravity for radial motions.
Comments: LaTex 22 pages, one figure
Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics of Galaxies (astro-ph.GA); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1704.00780 [gr-qc]

 

[atyy]

https://arxiv.org/abs/1704.01141
Finite entanglement entropy and spectral dimension in quantum gravity
Michele Arzano, Gianluca Calcagni
(Submitted on 4 Apr 2017 (v1), last revised 6 Apr 2017 (this version, v2))
What are the conditions on a spacetime geometry leading to a finite entanglement entropy density? We prove a very general result based on the analytic properties of the spectral zeta function of the theory: If the spectral dimension of the spatial boundary flows to zero at any scale, then the entanglement entropy cannot be finite. On one hand, this conclusion negatively affects a wide class of theories with ultraviolet (UV) finite two-point functions, including some models with compact momentum space, non-local quantum gravity and many states of quantum geometry in discrete combinatorial approaches such as loop quantum gravity, spin foams and group field theory (GFT). Possible ways out are considered. On the other hand, the above necessary condition agrees with the finding of a finite entropy density in string theory. We show that also multi-fractional theories yield a finite entanglement entropy density, even in the cases where the propagator is not particularly well behaved in the UV.

https://arxiv.org/abs/1704.02404
An algorithm for quantum gravity phenomenology
Yuri Bonder
(Submitted on 7 Apr 2017)
Quantum gravity phenomenology is the strategy towards quantum gravity where the priority is to make contact with experiments. Here I describe what I consider to be the best procedure to do quantum gravity phenomenology. The key step is to have a generic parametrization which allows one to perform self-consistency checks and to deal with many different experiments. As an example I describe the role that the Standard Model Extension has played when looking for Lorentz violation.

https://arxiv.org/abs/1704.02905
CDT and the Big Bang
J. Ambjorn, Y. Watabiki
(Submitted on 10 Apr 2017)
We describe a CDT-like model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four "magical" Jordan algebras of 3x3 Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10.

 

[atyy]

https://arxiv.org/abs/1704.03691
Towards a Cosmological subsector of Spin Foam Quantum Gravity
Benjamin Bahr, Sebastian Kloser, Giovanni Rabuffo
(Submitted on 12 Apr 2017)
We examine the four dimensional path integral for Euclidean quantum gravity in the context of the EPRL-FK spin foam model. The state sum is restricted to certain symmetric configurations which resembles the geometry of a flat homogeneous and isotropic universe. The vertex structure is specially chosen so that a basic concept of expansion and contraction of the lattice universe is allowed.
We compute the asymptotic form of the spin foam state sum in the symmetry restricted setting, and recover a Regge-type action, as well as an explicit form of the Hessian matrix, which captures quantum corrections. We investigate the action in the three cases of vacuum, a cosmological constant, and coupled to dust, and find that in all cases, the corresponding FRW dynamics is recovered in the limit of large lattices. While this work demonstrates a large intersection with computations done in the context of cosmological modelling with Regge Calculus, it is ultimately a setup for treating curved geometries in the renormalization of the EPRL-FK spin foam model.

 

[atyy]

https://arxiv.org/abs/1704.04067
From Coarse-Graining to Holography in Loop Quantum Gravity
Etera R. Livine
(Submitted on 13 Apr 2017)
We discuss the relation between coarse-graining and the holographic principle in the framework of loop quantum gravity and ask the following question: when we coarse-grain arbitrary spin network states of quantum geometry, are we integrating out physical degrees of freedom or gauge degrees of freedom? Focusing on how bulk spin network states for bounded regions of space are projected onto boundary states, we show that all possible boundary states can be recovered from bulk spin networks with a single vertex in the bulk and a single internal loop attached to it. This partial reconstruction of the bulk from the boundary leads us to the idea of realizing the Hamiltonian constraints at the quantum level as a gauge equivalence reducing arbitrary spin network states to one-loop bulk states. This proposal of "dynamics through coarse-graining" would lead to a one-to-one map between equivalence classes of physical states under gauge transformations and boundary states, thus defining holographic dynamics for loop quantum gravity.

 

[kodama]

Interpreting the isolated horizon boundary condition in terms of higher gauge theory
Thomas Zilker
(Submitted on 16 Mar 2017)
The purpose of this letter is to point out a relation between the boundary condition satisfied by spherically symmetric isolated horizons (formulated in terms of Ashtekar-Barbero variables) and the source-target matching condition (also known as fake flatness condition) in higher gauge theory. This relation may prove useful in the attempt to quantize the isolated horizon boundary condition which is in turn a possible starting point for the search for black hole solutions in the full theory of loop quantum gravity. Also, since a 2-connection is the mathematical object required for describing the parallel transport of 1-dimensional objects, the relation presented in this letter may provide further insight into the coupling of LQG to string-like objects investigated in other contexts.
Comments: 4 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Cite as: arXiv:1703.05620 [gr-qc]
(or arXiv:1703.05620v1 [gr-qc] for this version)

Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
Marc Geiller
(Submitted on 14 Mar 2017)
Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bulk-boundary correspondences. In particular, it has been acknowledged for quite some time that boundaries can break gauge invariance, and thereby turn gauge degrees of freedom into physical ones. There is however no known systematic way of identifying these degrees of freedom and possible associated boundary observables. Following recent work by Donnelly and Freidel, we show that this can be achieved by extending the covariant Hamiltonian formalism so as to make it gauge-invariant under arbitrary large gauge transformations. This can be done at the expense of introducing new boundary fields, which in turn determine new boundary symmetries and observables. We present the general framework behind this construction, and find the conditions under which it can be applied to an arbitrary Lagrangian. By studying the example of Abelian Chern-Simons theory, we then show that the new boundary observables in this case are nothing but the edge currents that are known to describe quantum Hall states. In three-dimensional gravity, the non-Abelian nature of the gauge transformations does however lead to a richer boundary theory. We derive the new boundary observables and show that they satisfy a covariant ISU(2) Kac-Moody affine algebra. We expect that this will play a major role for the quantization of gravity in finite regions.
Comments: 50+7 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1703.04748 [gr-qc]
(or arXiv:1703.04748v1 [gr-qc] for this version)

 

[kodama]

On effective loop quantum geometry of Schwarzschild interior
Jerónimo Cortez, William Cuervo, Hugo A. Morales-Técotl, Juan C. Ruelas
(Submitted on 11 Apr 2017)
The success of loop quantum cosmology to resolve classical singularities of homogeneous models has led to its application to the classical Schwarzschild black hole interior, which takes the form of a homogeneous Kantowski-Sachs model. The first steps of this were done in pure quantum mechanical terms, hinting at the traversable character of the would-be classical singularity, and then others were performed using effective heuristic models capturing quantum effects that allowed a geometrical description closer to the classical one but avoided its singularity. However, the problem of establishing the link between the quantum and effective descriptions was left open. In this work, we propose to fill in this gap by considering the path-integral approach to the loop quantization of the Kantowski-Sachs model corresponding to the Schwarzschild black hole interior. We show that the transition amplitude can be expressed as a path integration over the imaginary exponential of an effective action which just coincides, under some simplifying assumptions, with the heuristic one. Additionally, we further explore the consequences of the effective dynamics. We prove first that such dynamics imply some rather simple bounds for phase-space variables, and in turn, remarkably, in an analytical way, they imply that various phase-space functions that were singular in the classical model are now well behaved. In particular, the expansion rate, its time derivative, and the shear become bounded, and hence the Raychaudhuri equation is finite term by term, thus resolving the singularities of classical geodesic congruences. Moreover, all effective scalar polynomial invariants turn out to be bounded.
Comments: 26 pages, matches the PRD published version
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Phys.Rev. D95 (2017) no.6, 064041
DOI: 10.1103/PhysRevD.95.064041
Cite as: arXiv:1704.03362 [gr-qc]

 

[kodama]

New boundary variables for classical and quantum gravity on a null surface
Wolfgang Wieland
(Submitted on 24 Apr 2017)
The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical variables appear: a spinor and a spinor-valued two-form that encode the entire intrinsic geometry of the null surface. At a two-dimensional cross-section of the boundary, quasi-local expressions for the generators of two-dimensional diffeomorphisms, time translations, and dilatations of the null normal are introduced and written in terms of the new boundary variables. In addition, a generalisation of the first-law of black-hole thermodynamics for arbitrary null surfaces is found, and the relevance of the framework for non-perturbative quantum gravity is stressed and explained.
Comments: 41 pages, one figure
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1704.07391 [gr-qc]
(or arXiv:1704.07391v1 [gr-qc] for this version)

 

[atyy]

https://arxiv.org/abs/1705.01554
SYK-like Tensor Models on the Lattice
Prithvi Narayan, Junggi Yoon
(Submitted on 3 May 2017)
We study large N tensor models on lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it as a tensor model on four sites) and also a new model which interpolates between these two models. In each model, we evaluate various four point functions at large N and strong coupling, and discuss their spectrum and long time behaviours. We find similarities as well as differences from SYK model. We also generalize our analysis to rank-D tensor models where we obtain analogous results as D=3 case for the four point functions which we computed. For D>5, we are able to compute the next-to-subleading 1/N corrections for a specific four point function.

https://arxiv.org/abs/1705.01848
Impact of topology in foliated Quantum Einstein Gravity
W.B. Houthoff, A. Kurov, F. Saueressig
(Submitted on 4 May 2017)
We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale-dependence of Newton's coupling and the cosmological constant on a background spacetime with topology S^1xS^d. The resulting beta functions possesses a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology S^1xT^d and establishes that the flow is essentially independent of the background topology.

 

[atyy]

https://arxiv.org/abs/1705.01964
Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
Muxin Han, Shilin Huang
(Submitted on 4 May 2017)
In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ⟩ using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement R\'enyi entropy of |Ψ⟩ is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting R\'enyi entropy Sn of |Ψ⟩ approximates with high precision the R\'enyi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate CFT ground state.

 

[atyy]

https://arxiv.org/abs/1705.02685
Conformal Anomaly and Off-Shell Extensions of Gravity
Krzysztof A. Meissner, Hermann Nicolai
(Submitted on 7 May 2017)
The gauge dependence of the conformal anomaly for spin 3/2 and spin 2 fields in non-conformal supergravities has been a long standing puzzle. In this Letter we argue that the `correct' gauge choice is the one that follows from requiring all terms that would imply a violation of the Wess-Zumino consistency condition to be absent in the counterterm, because otherwise the usual link between the anomaly and the one-loop divergence becomes invalid. Remarkably, the `good' choice of gauge is the one that confirms our previous result that a complete cancellation of conformal anomalies in D=4 can only be achieved for N-extended (Poincar\'e) supergravities with N≥5.

 

[atyy]

https://arxiv.org/abs/1705.05558
Functional perturbative RG and CFT data in the ε-expansion
Alessandro Codello, Mahmoud Safari, Gian Paolo Vacca, Omar Zanusso
(Submitted on 16 May 2017)
We show how the use of standard perturbative RG allows for a renormalization group based computation of both the spectrum and the coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure by obtaining the leading and next-to-leading corrections in the ϵ-expansion of spectrum and OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multicritical models ϕ2n. The universal results explicitly match the ones recently derived in CFT frameworks.

https://arxiv.org/abs/1705.05417
Dimension and Dimensional Reduction in Quantum Gravity
S. Carlip
(Submitted on 15 May 2017)
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning of "dimension" and concluding with some speculative ideas of what dimensional reduction might mean for physics.

https://arxiv.org/abs/1705.05493
Quantum mechanix plus Newtonian gravity violates the universality of free fall
Matt Visser (Victoria University of Wellington)
(Submitted on 16 May 2017)
Classical point particles in Newtonian gravity obey, as they do in general relativity, the universality of free fall. However classical structured particles, (for instance with a mass quadrupole moment), need not obey the universality of free fall. Quantum mechanically, an elementary "point" particle can be described by a localized wave-packet, for which we can define a probability quadrupole moment. This probability quadrupole can, under plausible hypotheses, affect the universality of free fall. This raises an important issue of principle, as possible quantum violations of the universality of free fall would fundamentally impact on our ideas of what "quantum gravity" might look like. I will present an estimate of the size of the effect, and discuss where if at all it might be measured.

https://arxiv.org/abs/1705.05585
Measuring the effects of Loop Quantum Cosmology in the CMB data
Spyros Basilakos, Vahid Kamali, Ahmad Mehrabi
(Submitted on 16 May 2017)
In this Essay we investigate the observational signatures of Loop Quantum Cosmology (LQC) in the CMB data. First, we concentrate on the dynamics of LQC and we provide the basic cosmological functions. We then obtain the power spectrum of scalar and tensor perturbations in order to study the performance of LQC against the latest CMB data. We find that LQC provides a robust prediction for the main slow-roll parameters, like the scalar spectral index and the tensor-to-scalar fluctuation ratio, which are in excellent agreement within 1σ with the values recently measured by the Planck collaboration. This result indicates that LQC can be seen as an alternative scenario with respect to that of standard inflation.

https://arxiv.org/abs/1705.05696
Rotating black hole solutions in relativistic analogue gravity
Luca Giacomelli, Stefano Liberati
(Submitted on 16 May 2017)
Simulation and experimental realization of acoustic black holes in analogue gravity systems have lead to a novel understanding of relevant phenomena such as Hawking radiation or superradiance. We explore here the possibility to use relativistic systems for simulating rotating black hole solutions and possibly get an acoustic analogue of a Kerr black hole. In doing so we demonstrate a precise relation between non-relativistic and relativistic solutions and provide a new class of vortex solutions for relativistic systems. Such solutions might be used in the future as a test bed in numerical simulations as well as concrete experiments.

https://arxiv.org/abs/1705.05722
Quantum fluctuating geometries and the information paradox
Rodrigo Eyheralde, Miguel Campiglia, Rodolfo Gambini, Jorge Pullin
(Submitted on 16 May 2017)
We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking's original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when quantum corrections are taken into account, the profile of the Hawking radiation as a function of time contains information about the initial state of the collapsing shell. More work will be needed to determine if all the information can be recovered. The calculations show that non-trivial quantum effects can occur in regions of low curvature when horizons are involved, as for instance advocated in the firewall scenario.

 

[atyy]

https://arxiv.org/abs/1705.06654
Simplicial Palatini action
V.M. Khatsymovsky
(Submitted on 18 May 2017)
We consider the simplicial complex (piecewise flat spacetime) and a simplicial analog of the Palatini form of the general relativity action where the discrete Christoffel symbols are given on the tetrahedra (3-dimensional simplexes) as variables that are independent of the metric. Excluding these variables with the help of the equations of motion gives exactly the Hilbert-Einstein action or, in the present context, Regge action. The present paper continues our previous work. Now we include the parity violation term and the analogue of the Barbero-Immirzi parameter introduced in the Cartan-Weyl representation of the Einstein action with orthogonal connection. The path integral is considered and elementary areas are shown to be fixed at some Planck scale values.

https://arxiv.org/abs/1705.06711
Local Lorentz covariance in finite-dimensional Local Quantum Physics
Matti Raasakka
(Submitted on 18 May 2017)
We show that local Lorentz covariance arises canonically as the group of transformations between local thermal states in the framework of Local Quantum Physics, given the following three postulates: (i) Local observable algebras are finite-dimensional. (ii) Minimal local observable algebras are isomorphic to M2(C), the observable algebra of a single qubit. (iii) The vacuum restricted to any minimal local observable algebra is thermal. The derivation reveals a new and surprising relation between spacetime structure and local quantum states. In particular, we show how local restrictions of the vacuum can determine the connection between different local inertial reference frames.

https://arxiv.org/abs/1705.06407
Spacetime has a `thickness'
Samir D. Mathur
(Submitted on 18 May 2017)
Suppose we assume that (a) information about a black hole is encoded in its Hawking radiation and (b) causality is not violated to leading order in gently curved spacetime. Then we argue that spacetime cannot just be described as a manifold with a shape; it must be given an additional attribute which we call `thickness'. This thickness characterizes the spread of the quantum gravity wavefunctional in superspace -- the space of all 3-geometries. Low energy particles travel on spacetime without noticing the thickness parameter, so they just see an effective manifold. Objects with energy large enough to create a horizon do notice the finite thickness; this modifies the semiclassical evolution in such a way that we avoid horizon formation and the consequent violation of causality.

 

[kodama]

Signatures of extra dimensions in gravitational waves
David Andriot, Gustavo Lucena Gómez
(Submitted on 24 Apr 2017)
Considering gravitational waves propagating on the most general 4+N-dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves. All wave equations are derived in general and discussed. On Minkowski4 times an arbitrary Ricci-flat compact manifold, we find: a massless wave with an additional polarization, the breathing mode, and extra waves with high frequencies fixed by Kaluza-Klein masses. We discuss whether these two effects could be observed.
Comments: 21 pages + appendices, comments welcome!
Subjects: High Energy Physics - Theory (hep-th); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Astrophysical Phenomena (astro-ph.HE); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:1704.07392 [hep-th]
(or arXiv:1704.07392v1 [hep-th] for this version)

 

[kodama]

Area Operator in Loop Quantum Gravity
Adrian P. C. Lim
(Submitted on 10 May 2017)
A hyperlink is a finite set of non-intersecting simple closed curves in R×R3. Let S be an orientable surface in R3. The dynamical variables in General Relativity are the vierbein e and a su(2)×su(2)-valued connection ω. Together with Minkowski metric, e will define a metric g on the manifold. Denote AS(e) as the area of S, for a given choice of e.
The Einstein-Hilbert action S(e,ω) is defined on e and ω. We will quantize the area of the surface S by integrating AS(e) against a holonomy operator of a hyperlink L, disjoint from S, and the exponential of the Einstein-Hilbert action, over the space of vierbeins e and su(2)×su(2)-valued connections ω. Using our earlier work done on Chern-Simons path integrals in R3, we will write this infinite dimensional path integral as the limit of a sequence of Chern-Simons integrals. Our main result shows that the area operator can be computed from a link-surface diagram between L and S. By assigning an irreducible representation of su(2)×su(2) to each component of L, the area operator gives the total net momentum impact on the surface S.
Comments: arXiv admin note: text overlap with arXiv:1701.04397, arXiv:1705.00396
Subjects: Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG)
MSC classes: 83C45, 81S40, 81T45, 57R56
Cite as: arXiv:1705.06577 [math-ph]
Renormalizability, fundamentality and a final theory: The role of UV-completion in the search for quantum gravity
Karen Crowther, Niels Linnemann
(Submitted on 18 May 2017)
Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity (QG), where novel empirical data is lacking. One principle widely adopted in the search for QG is UV completion: the idea that a theory should (formally) hold up to all possible high energies. We argue---\textit{contra} standard scientific practice---that UV-completion is poorly-motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV completion is used, and how it should be used, in various specific approaches to QG.
Subjects: History and Philosophy of Physics (physics.hist-ph); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1705.06777 [physics.hist-ph]
(or arXiv:1705.06777v1 [physics.hist-ph] for this version)
mprint of quantum gravity in the dimension and fabric of spacetime
Giovanni Amelino-Camelia, Gianluca Calcagni, Michele Ronco
(Submitted on 13 May 2017)
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within the framework of multifractional theories, whose key assumption is an anomalous scaling of the spacetime dimension in the ultraviolet and a slow change of the dimension in the infrared. This sole ingredient is enough to produce a scale-dependent deformation of the integration measure with also a fuzzy spacetime structure. We also compare the multifractional correction to lengths with the types of Planckian uncertainty for distance and time measurements that was reported in studies combining quantum mechanics and general relativity heuristically. This allows us to fix two free parameters of the theory and leads, in one of the scenarios we contemplate, to a value of the ultraviolet dimension which had already found support in other quantum-gravity analyses. We also formalize a picture such that fuzziness originates from a fundamental discrete scale invariance at short scales and corresponds to a stochastic spacetime geometry, recovering the structure of Nottale scale relativity.
Comments: 5 pages
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1705.04876 [hep-th]
(or arXiv:1705.04876v1 [hep-th] for this version

 

[kodama]

The Thiemann Complexifier in Loop Cosmology
Jibril Ben Achour, Etera R. Livine
(Submitted on 10 May 2017)
In the context of Loop Quantum Gravity (LQG), we study the fate of the complexifier, that is the generator of the canonical transformations shifting the Immirzi parameter, for the homogeneous and isotropic FRW cosmology. We focus on the closed CVH algebra for canonical general relativity consisting in the complexifier, the 3d volume and the Hamiltonian constraint. In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a su(1,1) Lie algebra, with the Hamiltonian as a null generator and the complexifier as a boost. The su(1,1) Casimir is given by the matter density. In the loop gravity cosmology approach, the gravitational Hamiltonian is regularized in terms of SU(2) holonomies. In order to keep a closed CVH algebra, we show that the complexifier and inverse volume factor needs to be similarly regularized. Then the su(1,1) Casimir is given by the matter density and the volume gap. The action of the Hamiltonian constraints and the complexifier can be exactly integrated. This is straightforward to extend to the quantum level: the cosmological evolution is described in terms of SU(1,1) coherent states and the regularized complexifier generates unitary transformations. This means that, in the physical Hilbert space, the Immirzi ambiguity is to be distinguished from the volume gap, it can be rescaled unitarily and ultimately disappears from physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale transformations.
Comments: 37 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1705.03772 [gr-qc]
(or arXiv:1705.03772v1 [gr-qc] for this version)

 

[kodama]

Pre-inflationary universe in loop quantum cosmology
Tao Zhu, Anzhong Wang, Gerald Cleaver, Klaus Kirsten, Qin Sheng
(Submitted on 22 May 2017)
The evolutions of the flat FLRW universe and its linear perturbations are studied systematically in {\em the dressed metric approach} of LQC. When the evolution of the background at the quantum bounce is dominated by the kinetic energy of the inflaton, it can be divided into three different phases prior to the preheating, {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential dominated case such a universality is lost. It is also because of this universality that the linear perturbations are independent of the inflationary models, too, and are obtained exactly. During the transition phase, the evolution of the background is first matched to that given in other two phases, whereby the e-folds of the expansion are obtained. In this phase the perturbation modes are all oscillating, and are matched to the ones given in other phases. Considering two different sets of initial conditions, one is imposed during the contracting phase and the other is at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the pre-inflationary dynamics, the scalar and tensor power spectra become scale-dependent. Comparing with the Planck 2015 data, we find constraints on the total e-folds that the universe must have expanded since the bounce, in order to be consistent with current observations.
Comments: revtex4, 24 figures, and 5 tables
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1705.07544 [gr-qc]
(or arXiv:1705.07544v1 [gr-qc] for this version)

 

[atyy]

https://arxiv.org/abs/1705.08581
The ıε prescription in the SYK model
Razvan Gurau
(Submitted on 24 May 2017)
We introduce an ıϵ prescription for the SYK model both at finite and at zero temperature. This prescription regularizes all the naive ultraviolet divergences of the model. As expected, the prescription breaks the conformal invariance, but the latter is restored in the ϵ→0 limit. We prove rigorously that in the limit ϵ→0 the Schwinger Dyson equation of the resummed two point at low momentum is recovered.

 

[MTd2]

https://arxiv.org/abs/1705.09030

Einstein Equation from Covariant Loop Quantum Gravity and Semiclassical Continuum Limit
Muxin Han
(Submitted on 25 May 2017)
In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of Einstein equation can be approached by dominant configurations in spinfoam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spinfoam formulation, and how to take advantage of it.

 

[atyy]

https://arxiv.org/abs/1705.09141
Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
Olivier J. Veraguth, Charles H.-T. Wang
(Submitted on 25 May 2017)
Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field providing the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. In this work, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. Specifically, we introduce a "conformal Einstein frame" in which loop quantization is implemented and demonstrate that different Immirzi parameters under this description are associated with different conformal frames related by a global conformal transformation. Nevertheless, they share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field.

https://arxiv.org/abs/1705.09208
What are we missing in our search for quantum gravity?
Lee Smolin
(Submitted on 25 May 2017)
Some reflections are presented on the state of the search for a quantum theory of gravity. I discuss diverse regimes of possible quantum gravitational phenomenon, some well explored, some novel.

https://arxiv.org/abs/1705.08959
Gravity from Quantum Spacetime by Twisted Deformation of the Quantum Poincaré Group
Cesar A. Aguillón, Albert Much, Marcos Rosenbaum, J. David Vergara
(Submitted on 24 May 2017)
We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from Quantum Gravity. Specifically we consider a two-parameter class of twisted Poincar\'e algebras, from which Lie-algebraic noncommutativities of the translations are derived as well as associative star-products, deformed Riemannian geometries, Lie-algebraic twisted Minkowski spaces and quantum effects that arise as noncommutativities. Starting from a universal differential algebra of forms based on the above mentioned Lie-algebraic noncommutativities of the translations, we construct the noncommutative differential forms and Inner and Outer derivations, which are the noncommutative equivalents of the vector fields in the case of commutative differential geometry. Having established the essentials of this formalism we construct a bimodule, required to be central under the action of the Inner derivations in order to have well defined contractions and from where the algebraic dependence of its coefficients is derived. This again then defines the noncommutative equivalent of the geometrical line-element in commutative differential geometry. We stress, however, that even though the components of the twisted metric are by construction symmetric in their algebra valuation, this is not so for their inverse and thus to construct it we made use of Gel'fand's theory of quasi-determinants, which is conceptually straightforward but computationally becoming quite complicate beyond an algebra of 3 generators. The consequences of the noncommutativity of the Lie-algebra twisted geometry are further discussed.

 

[kodama]

Loop Quantum Gravity in the Momentum Representation
W. F. Chagas-Filho
(Submitted on 26 May 2017)
We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations that can be interpreted as describing quantum gravity in the momentum representation.
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1705.09471 [gr-qc]

 

[kodama]

No alternative to proliferation
Daniele Oriti
(Submitted on 27 May 2017)
We reflect on the nature, role and limits of non-empirical theory assessment in fundamental physics, focusing in particular on quantum gravity. We argue for the usefulness and, to some extent, necessity of non-empirical theory assessment, but also examine critically its dangers. We conclude that the principle of proliferation of theories is not only at the very root of theory assessment but all the more necessary when experimental tests are scarce, and also that, in the same situation, it represents the only medicine against the degeneration of scientific research programmes.
Comments: 15 pages; contribution to the volume "Why trust a theory?", edited by: R. Dardashti, R. Dawid, K. Thebault, to be published by Cambridge University Press
Subjects: History and Philosophy of Physics (physics.hist-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1705.09858 [physics.hist-ph]

 

[kodama]

Renormalization and Coarse-graining of Loop Quantum Gravity
Christoph Charles
(Submitted on 31 May 2017)
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will investigate some coarse-graining methods that should become helpful in this enterprise. We concentrate on two aspects of the theory's coarse-graining: finding natural large scale observables on one hand and studying how the dynamics of varying graphs could be cast onto fixed graphs on the other hand.
To determine large scale observables, we study the case of hyperbolic tetrahedra and their natural description in a language close to loop quantum gravity. The surface holonomies in particular play an important role. This highlights the structure of double spin networks, which consist in a graph and its dual, which seems to also appear in works from Freidel et al. To solve the problem of varying graphs, we consider and define loopy spin networks. They encode the local curvature with loops around an effective vertex and allow to describe different graphs by hidding them in a coarse-graining process. Moreover, their definition gives a natural procedure for coarse-graining allowing to relate different scales.
Together, these two results constitute the foundation of a coarse-graining programme for diffeomorphism invariant theories.
Comments: PhD Thesis, Ecole Normale Superieure de Lyon, 303pages, many figures
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1705.10984 [gr-qc]
(or arXiv:1705.10984v1 [gr-qc] for this version)

 

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The continuum approach to the BF vacuum: the U(1) case
Patryk Drobiński, Jerzy Lewandowski
(Submitted on 27 May 2017)
A quantum representation of holonomies and exponentiated fluxes of a U(1) gauge theory that contains the Pullin-Dittrich-Geiller (DG) vacuum is presented and discussed. Our quantization is performed manifestly in a continuum theory, without any discretization. The discretness emerges on the quantum level as a property of the spectrum of the quantum holonomy operators. The new type of a cylindrical consistency present in the DG approach, now follows easily and naturally. A generalization to the non--Abelian case seems not difficult.
Comments: 12 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1705.09836 [gr-qc]

 

[kodama]

Diffeomorphism invariant cosmological sector in loop quantum gravity
Christopher Beetle, Jonathan Steven Engle, Matthew Ernest Hogan, Phillip Mendonca
(Submitted on 8 Jun 2017)
In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented.
Comments: 25 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1706.02424 [gr-qc]
(or arXiv:1706.02424v1 [gr-qc] for this version)

 

[kodama]

Pulsations of a black hole in loop quantum gravity
Changjun Gao, Youjun Lu, You-Gen Shen, Valerio Faraoni
(Submitted on 24 Jun 2017)
The Hawking-Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using the corrected dynamical equation of loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually {an outer and an inner apparent horizon}, resembling the Reissner-Nordstr\"om situation. For a distant observer the {horizon} crossing occurs in an infinite time and the pulsations of the black hole quantum "beating heart" are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.
Comments: 24 pages, 2 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1706.08009 [gr-qc]

 

[atyy]

https://arxiv.org/abs/1706.09833
Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics
Andrea Dapor, Klaus Liegener
(Submitted on 29 Jun 2017)
The concept of effective dynamics has proven successful in LQC, the cosmological sector of LQG. We apply the same idea in the full theory, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson-Walker spacetime. We comment on the relation with effective LQC and find a deviation stemming from the Lorentzian part of the Hamiltonian.

 

[kodama]

Quantum Reduced Loop Gravity with matter: eigenvectors of the Hamiltonian operator in isotropic cosmology
Jakub Bilski, Suddhasattwa Brahma, Antonino Marciano
(Submitted on 30 Jun 2017)
Introducing a new method, we demonstrate how the action of reduced operators can be derived without resorting to a recoupling theory and how they exactly reproduce the results obtained in the standard approach of Quantum Reduced Loop Gravity (QRLG). This is particularly relevant while dealing with volume operator when dealing with the coupling of matter fields to gravity. Apart from reinforcing the close link between QRLG and loop quantum cosmology (LQC), this procedure also sheds new light on the issue of how to extract the continuum limit, without resorting to the large-jexpansion, thereby pointing towards a new approach to tackle this problem.
Comments: 14 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1707.00065 [gr-qc]
(or arXiv:1707.00065v1 [gr-qc] for this version)

 

[kodama]

2+1 homogeneous Loop Quantum Gravity with a scalar field clock
Jakub Bilski, Antonino Marciano
(Submitted on 3 Jul 2017 (v1), last revised 5 Jul 2017 (this version, v2))
We focus on three-dimensional QRLG with the purpose of shedding light on the link between reduced LQG and LQC in four space-time dimensions. Considering homogeneous three-dimensional LQG, the theory simplifies to QRLG. We then implement Thiemann's Quantum Spin Dynamics for Euclidean three-dimensional space-time in presence of a real scalar matter field. We deploy a polymer quantization of the scalar field while using methods of quantum reduced loop gravity. We compute the scalar Hamiltonian operator on the states of the kinematical Hilbert space of the theory, and exhibit its matrix elements that are derived using a new simplified method. The coupling to matter, which plays the role of a carrier of dynamics, opens the pathway to the study of phenomenological implications. We finally comment on the relations between three-dimensional QRLG and LQC, as well as on the appearance of the correspondence principle for the scalar field.
Comments: 15 pages, typos corrected, cross-citation added
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1707.00723 [gr-qc]

 

[kodama]

A new duality between Topological M-theory and Loop Quantum Gravity
Andrea Addazi, Antonino Marciano
(Submitted on 17 Jul 2017)
Inspired by the long wave-length limit of topological M-theory, which re-constructs the theory of 3+1D gravity in the self-dual variables' formulation, we conjecture the existence of a duality between Hilbert spaces, the H-duality, to unify topological M-theory and loop quantum gravity (LQG). By H-duality non-trivial gravitational holonomies of the kinematical Hilbert space of LQG correspond to space-like M-branes. The spinfoam approach captures the non-perturbative dynamics of space-like M-branes, and can be claimed to be dual to the S-branes foam. The Hamiltonian constraint dealt with in LQG is reinterpreted as a quantum superposition of SM-brane nucleations and decays.
Subjects: High Energy Physics - Theory (hep-th)
Cite as: arXiv:1707.05347 [hep-th]

 

[kodama]

Induced loop quantum cosmology on a brane via holography
C. A. S. Silva
(Submitted on 20 Jul 2017)
Based on the holographic principle, it is demonstrated that loop quantum Friedmann equations can be induced on a brane, corresponding to a strongly coupled string regime in the bulk, and have braneworld cosmology equations as its low energy limit. Such result can establish a possible connection between loop quantum gravity and string theory.
Comments: 6 pages, 1 figure
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1707.07586 [gr-qc]

 

[atyy]

https://arxiv.org/abs/1708.01380
Kochen-Specker theorem revisited
Del Rajan (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)
(Submitted on 4 Aug 2017)
The Kochen-Specker theorem is a basic and fundamental 50 year old non-existence result affecting the foundations of quantum mechanix, strongly implying the lack of any meaningful notion of "quantum realism", and typically leading to discussions of "contextuality" in quantum physics. Original proofs of the Kochen-Specker theorem proceeded via brute force counter-examples; often quite complicated and subtle (albeit mathematically "elementary") counter-examples. Only more recently have somewhat more "geometrical" proofs been developed. We present herein yet another simplified geometrical proof of the Kochen-Specker theorem, one that is valid for any number of dimensions, that minimizes the technical machinery involved, and makes the seriousness of the issues raised manifest.

 

[atyy]

https://arxiv.org/abs/1708.07445
Towards the map of quantum gravity
Jakub Mielczarek, Tomasz Trześniewski
(Submitted on 24 Aug 2017 (v1), last revised 5 Oct 2017 (this version, v2))
In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations, Ho\v{r}ava-Lifshitz gravity, Asymptotic Safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincar\'{e} algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.

https://arxiv.org/abs/1708.07716
Extended Phase Space Analysis of Interacting Dark Energy Models in Loop Quantum Cosmology
Hmar Zonunmawia, Wompherdeiki Khyllep, Nandan Roy, Jibitesh Dutta, Nicola Tamanini
(Submitted on 25 Aug 2017)
The present work deals with the dynamical system investigation of interacting dark energy models (quintessence and phantom) in the framework of Loop Quantum Cosmology by taking into account a broad class of self-interacting scalar field potentials. The main reason for studying potentials beyond the exponential type is to obtain additional critical points which can yield more interesting cosmological solutions. The stability of critical points and the asymptotic behavior of the phase space are analyzed using dynamical system tools and numerical techniques. We study two class of interacting dark energy models and consider two specific potentials as examples: the hyperbolic potential and the inverse power-law potential. We found a rich and interesting phenomenology including the avoidance of big rip singularities due to loop quantum effects, smooth and non-linear transitions from matter domination to dark energy domination and finite periods of phantom domination with dynamical crossing of the phantom barrier.

https://arxiv.org/abs/1708.08667
A non-polynomial gravity formulation for Loop Quantum Cosmology bounce
Stefano Chinaglia, Aimeric Colleaux, Sergio Zerbini
(Submitted on 29 Aug 2017 (v1), last revised 5 Sep 2017 (this version, v2))
Recently the so-called mimetic gravity approach has been used to obtain corrections to Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists in adding geometric non-polynomial higher derivative terms to Hilbert-Einstein action, which are nonetheless polynomials and lead to second order differential equation in Friedmann-Lema\^itre-Robertson-Walker spacetimes. Our explicit action turns out to be a realization of the Helling proposal of effective action with infinite number of terms. The model is investigated also in presence of non vanishing cosmological constant and a new exact bounce solution is found and studied.

https://arxiv.org/abs/1709.03242
Noncommutativity in Effective Loop Quantum Cosmology
Abraham Espinoza-García (UPIIG-IPN, México), Efraín Torres-Lomas (UG, México)
(Submitted on 11 Sep 2017 (v1), last revised 12 Sep 2017 (this version, v2))
We construct two noncommutative extensions of the Loop Quantum Cosmology effective scheme for the open FLRW model with a standard scalar field with quadratic potential. Firstly, noncommutativity is implemented in the configuration sector only (among the holonomy variable and the matter degree of freedom). We show that this type of noncommutativity seems to retain key features of the Loop Quantum Cosmology paradigm for a free field; however, when considering the addition of a quadratic potential,this compatibility weakens regarding the trajectories followed by the scalar field. Secondly, noncommutativity is implemented in the momentum sector (among the momentum associated to the holonomy variable and the momentum associated to the matter field). In the free case, the only effect of this noncommutativity is that of making the volume function to grow faster, retaining key features of the Loop Quantum Cosmology paradigm. We show that, when considering a quadratic potential, this second kind of noncommutativity is more favored than the first one in regard to the trajectories followed by the scalar field.

https://arxiv.org/abs/1709.06331
Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
Alec Yonika, Gaurav Khanna, Parampreet Singh
(Submitted on 19 Sep 2017)
Though loop quantization of several spacetimes has exhibited existence of a bounce via an explicit evolution of states using numerical simulations, the question about the black hole interior has remained open. To answer this question, it is important to first understand the stability of the quantum Hamiltonian constraint. We take first steps towards addressing these issues for a loop quantization of the Schwarzschild interior. The von-Neumann stability analysis is performed using separability of solutions as well as a full two dimensional quantum difference equation. This results in a condition which translates to stability for black holes which have a very large mass compared to the Planck mass. In addition, stability analysis leads to a constraint on the localization of the allowed states. With the caveat of using kinematical norm, Gaussian states are evolved using the quantum difference equation and singularity resolution is obtained. Bounce is found for one of the triad variables, but for the other triad variable singularity resolution amounts to a non-singular passage through the zero volume. States are found to be peaked at the classical trajectory for a long time before and after the singularity resolution, and retain their semi-classical character across the zero volume.

https://arxiv.org/abs/1709.08370
Random Invariant Tensors
Youning Li, Muxin Han, Dong Ruan, Bei Zeng
(Submitted on 25 Sep 2017)
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon of `concentration of measure', saying that for any bipartition, the expected value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimension goes to infinity. This is also true even when the average is over the invariant subspace instead of the whole space for 4−valent tensors, although its entropy deficit is divergent. One might expect that for n≥5, n−valent random invariant tensor would behavior similarly. However, we show that, the expected entropy deficit of reduced density matrix of such n−valent random invariant tensor from maximum, is not divergent but a finite number. Under some special situation, the number could be even smaller than half a bit, which is the deficit of random pure state over the whole Hilbert space from maximum.

https://arxiv.org/abs/1709.08511
Intertwiner Entanglement on Spin Networks
Etera R. Livine
(Submitted on 25 Sep 2017)
In the context of quantum gravity, we clarify entanglement calculations on spin networks: we distinguish the gauge-invariant entanglement between intertwiners located at the nodes and the entanglement between spin states located on the network's links. We compute explicitly these two notions of entanglement between neighboring nodes and show that they are always related to the typical ln(2j+1) term depending on the spin j living on the link between them. This ln(2j+1) contribution comes from looking at non-gauge invariant states, thus we interpret it as gauge-breaking and unphysical. In particular, this confirms that pure spin network basis states do not carry any physical entanglement, so that true entanglement and correlations in loop quantum gravity comes from spin or intertwiner superpositions.

https://arxiv.org/abs/1709.08989
Simplicity constraints: a 3d toy-model for Loop Quantum Gravity
Christoph Charles
(Submitted on 26 Sep 2017)
In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity constraints. Their geometrical interpretation is however unsatisfactory as they do not constitute a space-time connection. It would be possible to resolve this point by using a full Lorentz connection or, equivalently, by using the self-dual Ashtekar variables. This leads however to simplicity constraints or reality conditions which are notoriously difficult to implement in the quantum theory.
We explore in this paper the possibility of imposing such constraints at the quantum level in the context of canonical quantization. To do so, we define a simpler model, in 3d, with similar constraints by extending the phase space to include an independent vielbein. We define the classical model and show that a precise quantum theory by gauge-unfixing can be defined out of it, completely equivalent to the standard 3d euclidean quantum gravity.
We discuss possible future explorations around this model as it could help as a stepping stone to define full-fledged covariant Loop Quantum Gravity.

https://arxiv.org/abs/1709.09806
The emergence of 3+1D Einstein gravity from topological gravity
Zheng-Cheng Gu
(Submitted on 28 Sep 2017)
Quantum field theory successfully explains the origin of all fundamental forces except gravity due to the renormalizability and ultraviolet(UV) completion puzzles. The ADS/CFT correspondence conjecture might naturally resolve the above two puzzles for ADS space gravity. In this paper, we propose a topological scenario to resolve the above two puzzles for generic cases(e.g., with or without cosmological constant term). First, we propose a 3+1D topological (quantum) gravity theory which is perturbatively renormalizable and potentially UV complete, this step can be regarded as a straightforward generalization of Edward Witten's Chern-Simons theory proposal for 2+1D topological gravity. Then, we show that Einstein-Cartan equation and classical space-time naturally emerge from topological (quantum) gravity via loop condensation. The second step is a unique feature in 3+1D and it might even naturally explain why our space-time is four dimensional. Experimentally measurable low energy predictions are also discussed.

https://arxiv.org/abs/1710.04015
Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
Andrea Dapor, Klaus Liegener
(Submitted on 11 Oct 2017)
This is the first paper of a series dedicated to LQG coherent states and cosmology. The concept is based on the effective dynamics program of Loop Quantum Cosmology, where the classical dynamics generated by the expectation value of the Hamiltonian on semiclassical states is found to be in agreement with the quantum evolution of such states. We ask the question of whether this expectation value agrees with the one obtained in the full theory. The answer is in the negative. This series of papers is dedicated to detailing the computations that lead to that surprising result. In the current paper, we construct the family of coherent states in LQG which represent flat (k=0) Robertson-Walker spacetimes, and present the tools needed to compute expectation values of polynomial operators in holonomy and flux on such states. These tools will be applied to the LQG Hamiltonian operator (in Thiemann regularization) in the second paper of the series. The third paper will present an extension to k≠0 cosmologies and a comparison with alternative regularizations of the Hamiltonian.

https://arxiv.org/abs/1710.04473
Entanglement entropy and correlations in loop quantum gravity
Alexandre Feller, Etera R. Livine
(Submitted on 12 Oct 2017)
Black hole entropy is one of the few windows toward the quantum aspects of gravitation and its study over the years have highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations are being explored in terms of the entanglement entropy between regions of space. In the context of loop quantum gravity, this translates into the analysis of the correlations between regions of the spin network states defining the quantum state of geometry of space. In this paper, we explore a class of states, motivated by results in condensed matter physics, satisfying an area law for entanglement entropy and having non-trivial correlations. We highlight that entanglement comes from holonomy operators acting on loops crossing the boundary of the region.

https://arxiv.org/abs/1710.06195
On the volume simplicity constraint in the EPRL spin foam model
Benjamin Bahr, Vadim Belov
(Submitted on 17 Oct 2017)
We propose a quantum version of the quadratic volume simplicity constraint for the EPRL spin foam model. It relies on a formula for the volume of 4-dimensional polyhedra, depending on its bivectors and the knotting class of its boundary graph. While this leads to no further condition for the 4-simplex, the constraint becomes non-trivial for more complicated boundary graphs. We show that, in the semi-classical limit of the hypercuboidal graph, the constraint turns into the geometricity condition observed recently by several authors.

https://arxiv.org/abs/1711.04991
Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology
Yu Han, Molin Liu
(Submitted on 14 Nov 2017)
In the spatially flat case of loop quantum cosmology, the connection k¯ is usually replaced by the μ¯ holonomy sin(μ¯k)μ¯ in the effective theory. In this paper, instead of the μ¯ scheme, we use a generalised, undertermined function g(k¯,p¯) to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction on the form of g(k¯,p¯), then we derive the gauge invariant equations of motion of the scalar, tensor and vector perturbations and study the inflationary power spectra with generalised holonomy corrections.

https://arxiv.org/abs/1711.05693
Connecting Loop Quantum Gravity and String Theory via Quantum Geometry
Deepak Vaid
(Submitted on 15 Nov 2017)
We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macroscopic geometry emerges and String Theory then becomes the \emph{effective} theory which describes the dynamics of that exoskeleton. The core of the argument rests on the claim that the Nambu-Goto action of String Theory can be viewed as the expectation value of the LQG area operator evaluated on the string worldsheet.

https://arxiv.org/abs/1711.05967
A Renormalizable SYK-type Tensor Field Theory
Joseph Ben Geloun, Vincent Rivasseau
(Submitted on 16 Nov 2017)
In this paper we introduce a simple field theoretic version of the Carrozza-Tanasa-Klebanov-Tarnopolsky (CTKT) "uncolored" holographic tensor model. It gives a more familiar interpretation to the previously abstract modes of the SYK or CTKT models in terms of momenta. We choose for the tensor propagator the usual Fermionic propagator of condensed matter, with a spherical Fermi surface, but keep the CTKT interactions. Hence our field theory can also be considered as an ordinary condensed matter model with a non-local and non-rotational invariant interaction. Using a multiscale analysis we prove that this field theory is just renormalizable to all orders of perturbation theory in the ultraviolet regime.

https://arxiv.org/abs/1711.06085
Gravity Induced Non-Local Effects in the Standard Model
S. O. Alexeyev, X. Calmet, B. N. Latosh
(Submitted on 16 Nov 2017)
We show that the non-locality recently identified in quantum gravity using resummation techniques propagates to the matter sector of the theory. We describe these non-local effects using effective field theory techniques. We derive the complete set of non-local effective operators at order NG2 for theories involving scalar, spinor, and vector fields. We then use recent data from the Large Hadron Collider to set a bound on the scale of space-time non-locality and find M⋆>3×10−11 GeV.

 

[atyy]

https://arxiv.org/abs/1711.08482
AdS2 holography and the SYK model
Gábor Sárosi
(Submitted on 22 Nov 2017)
These are lecture notes based on a series of lectures presented at the XIII Modave Summer School in Mathematical physics aimed at PhD students and young postdocs. The goal is to give an introduction to some of the recent developments in understanding holography in two bulk dimensions, and its connection to microscopics of near extremal black holes. The first part reviews the motivation to study, and the problems (and their interpretations) with holography for AdS2 spaces. The second part is about the Jackiw-Teitelboim theory and nearly-AdS2 spaces. The third part introduces the Sachdev-Ye-Kitaev model, reviews some of the basic calculations and discusses what features make the model exciting.

https://arxiv.org/abs/1711.08470
Propagators for gauge-invariant observables in cosmology
Markus B. Fröb, William C. C. Lima
(Submitted on 22 Nov 2017)
We make a proposal for gauge-invariant observables in perturbative quantum gravity in cosmological spacetimes, building on the recent work of Brunetti et al. [JHEP 08 (2016) 032]. These observables are relational, and are obtained by evaluating the field operator in a field-dependent coordinate system. We show that it is possible to define this coordinate system such that the non-localities inherent in any higher-order observable in quantum gravity are causal, i.e., the value of the gauge-invariant observable at a point x only depends on the metric and inflation perturbations in the past light cone of x. We then construct propagators for the metric and inflaton perturbations in a gauge adapted to that coordinate system, which simplifies the calculation of loop corrections, and give explicit expressions for relevant cases: matter- and radiation-dominated eras and slow-roll inflation.

https://arxiv.org/abs/1711.09270
Loop Quantum Cosmology Corrected Gauss-Bonnet Singular Cosmology
K. Kleidis, V.K. Oikonomou
(Submitted on 25 Nov 2017)
In this work we investigate which Loop Quantum Cosmology corrected Gauss-Bonnet F(G) gravity can realize two singular cosmological scenarios, the intermediate inflation and the singular bounce scenarios. The intermediate inflation scenario has a Type III sudden singularity at t=0, while the singular bounce has a soft Type IV singularity. By using perturbative techniques, we find the holonomy corrected F(G) gravities that generate at leading order the aforementioned cosmologies and we also argue that the effect of the holonomy corrections is minor to the power spectrum of the primordial curvature perturbations of the classical theory.

https://arxiv.org/abs/1711.09941
Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
Goffredo Chirco, Daniele Oriti, Mingyi Zhang
(Submitted on 27 Nov 2017)
We consider the special case of Random Tensor Networks (RTN) endowed with gauge symmetry constraints on each tensor. We compute the R\`enyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background independent quantum gravity, and for importing quantum gravity tools in tensor network research.

https://arxiv.org/abs/1711.10861
The time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology
Beatriz Elizaga Navascués, Daniel Martín de Blas, Guillermo A. Mena Marugán
(Submitted on 29 Nov 2017)
Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the Planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to loop quantum cosmology with admissible ultraviolet behaviour leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. In spite of their similarities and relations, we show in this work that the effective equations that they provide for the evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the Big Bounce plays in loop quantum cosmology, e.g. as a natural instant of time to set initial conditions for the perturbations, we also analyze the positivity of the time-dependent mass when this bounce occurs. We prove that the mass of the tensor perturbations is positive in the hybrid approach when the kinetic contribution to the energy density of the inflaton dominates over its potential, as well as for a considerably large sector of backgrounds around that situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background solutions that includes the kinetically dominated ones, namely, the mass then is positive for the hybrid approach, whereas it typically becomes negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflaton mass that are phenomenologically favored.

https://arxiv.org/abs/1711.10943
The loop quantum cosmology bounce as a Kasner transition
Edward Wilson-Ewing
(Submitted on 29 Nov 2017)
For the Bianchi type I space-time (vacuum or with a massless scalar field), the loop quantum cosmology bounce can be viewed as a rapid transition between two classical solutions, with a simple transformation rule relating the Kasner exponents of the two epochs. This transformation rule can be extended to other Bianchi space-times under the assumption that during the loop quantum cosmology bounce the contribution of the spatial curvature to the Hamiltonian constraint is negligible compared to the kinetic terms. For the vacuum Bianchi type IX space-time there are transformation rules for how each of the parameters characterizing the Kasner epochs change during the bounce. This provides a quantum gravity extension to the Mixmaster dynamics of general relativity, and may have interesting implications for the Belinski-Khalatnikov-Lifshitz conjecture.

 

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https://arxiv.org/abs/1712.03677
Covariance and Anomaly-freedom in symmetry-reduced self dual models of Loop Quantum Gravity
Jibril Ben Achour, Suddhasattwa Brahma
(Submitted on 11 Dec 2017)
In effective models of loop quantum gravity (LQG), the curvature of the connection in the Hamiltonian constraint is regularised based on the holonomy of the connection, prior to quantization. At this very first step, whether the holonomy-corrected system of "first-class" constraints form a closed algebra such that they still act as generators of gauge transformations, and consequently eliminate the same number of spurious degrees of freedom, is a crucial question which needs to be clarified before dealing with quantum dynamics. In the real Ashtekar-Barbero framework, such holonomy-corrected models have typically a deformed notion of covariance when no local degrees of freedom are involved, and fail to be (gauge-)covariant in models exhibiting local physical degrees of freedom. Recently discovered no-go results in models involving non-perturbative inhomogeneity challenge the possibility of including holonomy modifications in realistic scenarios depicting gravitational collapse of scalar matter or cylindrical gravitational waves. Moreover, it is known that the inclusion of the μ¯-scheme, which implements a coarse-graining procedure at the effective level, leads to additional difficulties in such models. In this article, we show how such conclusions can be by-passed when working in the self dual formulation, i.e. we investigate the fate of covariance in holonomy-corrected models of LQG based on the original self dual Ashtekar formulation. We consider two systems of particular interest: spherically symmetric gravity minimally coupled to a scalar field and (unpolarized) Gowdy cosmology. Both have local degrees of freedom and, therefore, represent midisuperspace models beyond what has been studied in the LQG literature.

https://arxiv.org/abs/1712.06918
On the distribution of the eigenvalues of the area operator in loop quantum gravity
J. Fernando Barbero, Juan Margalef-Bentabol, Eduardo J. S. Villaseñor
(Submitted on 19 Dec 2017)
We study the distribution of the eigenvalues of the area operator in loop quantum gravity concentrating on the part of the spectrum relevant for isolated horizons. We first show that the approximations relying on integer partitions are not sufficient to obtain the asymptotic behaviour of the eigenvalue distribution for large areas. We then develop a method, based on Laplace transforms, that provides a very accurate solution to this problem. The representation that we get is valid for any area and can be used to obtain its asymptotics in the large area limit.

https://arxiv.org/abs/1712.07266
Cosmological evolution as squeezing: a toy model for group field cosmology
Eugene Adjei, Steffen Gielen, Wolfgang Wieland
(Submitted on 19 Dec 2017)
We present a simple model of quantum cosmology based on the group field theory (GFT) approach to quantum gravity. The model is formulated on a subspace of the GFT Fock space for the quanta of geometry, with a fixed volume per quantum. In this Hilbert space, cosmological expansion corresponds to the generation of new quanta. Our main insight is that the evolution of a flat FLRW universe with a massless scalar field can be described on this Hilbert space as squeezing, familiar from quantum optics. As in GFT cosmology, we find that the three-volume satisfies an effective Friedmann equation similar to the one of loop quantum cosmology, connecting the classical contracting and expanding solutions by a quantum bounce. The only free parameter in the model is identified with Newton's constant. We also comment on the possible topological interpretation of our squeezed states. This paper can serve an introduction into the main ideas of GFT cosmology without requiring the full GFT formalism; our results can also motivate new developments in GFT and its cosmological application.

 

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https://arxiv.org/abs/1801.00273
A new bound on polymer quantization via an opto-mechanical setup
M. Khodadi, K. Nozari, S. Dey, A. Bhat, Mir Faizal
(Submitted on 31 Dec 2017)
The existence of a minimal measurable length as a characteristic length in the Planck scale is one of the main features of quantum gravity and has been widely explored in the context. Various different deformations of spacetime have been employed successfully for the purpose. However, polymer quantization approach is a relatively new and dynamic field towards the quantum gravity phenomenology, which emerges from the symmetric sector of the loop quantum gravity. In this article, we extend the standard ideas of polymer quantization to find a new and tighter bound on the polymer deformation parameter. Our protocol relies on an opto-mechanical experimental setup that was originally proposed in Ref.\cite{ref:Igor} to explore some interesting phenomena by embedding the minimal length into the standard canonical commutation relation. We extend this scheme to probe the \emph{polymer length} deformed canonical commutation relation of the center of mass mode of a mechanical oscillator with a mass around the Planck scale. The method utilizes the novelty of exchanging the relevant mechanical information with a high intensity optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of the current technologies and, thus, it could uncover a decent realization of quantum gravitational phenomena thorough a simple table-top experiment.

https://arxiv.org/abs/1801.00768
Emergent de Sitter epoch of the quantum Cosmos
Mehdi Assanioussi, Andrea Dapor, Klaus Liegener, Tomasz Pawłowski
(Submitted on 2 Jan 2018)
The quantum nature of the Big Bang is reexamined in the framework of Loop Quantum Cosmology. The strict application of a regularization procedure to the Hamiltonian, originally developed for the Hamiltonian in loop quantum gravity, leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a flat expanding Universe.

https://arxiv.org/abs/1801.01479
Black Holes as Quantum Gravity Condensates
Daniele Oriti, Daniele Pranzetti, Lorenzo Sindoni
(Submitted on 4 Jan 2018)
We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalised condensate states, involving sums over arbitrarily refined graphs (dual to 3d triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.

https://arxiv.org/abs/1801.03027
Characteristic Time Scales for the Geometry Transition of a Black Hole to a White Hole from Spinfoams
Marios Christodoulou, Fabio D'Ambrosio
(Submitted on 9 Jan 2018)
Quantum fluctuations of the metric provide a decay mechanism for black holes, through a transition to a white hole geometry. Old perplexing results by Ambrus and H\'aj\'i\v{c}ek and more recent results by Barcel\'o, Carballo--Rubio and Garay, indicate a characteristic time scale of this process that scales linearly with the mass of the collapsed object. We compute the characteristic time scales involved in the quantum process using Lorentzian Loop Quantum Gravity amplitudes, corroborating these results but reinterpreting and clarifying their physical meaning. We first review and streamline the classical set up, and distinguish and discuss the different time scales involved. We conclude that the aforementioned results concern a time scale that is different from the lifetime, the latter being the much longer time related to the probability of the process to take place. We recover the exponential scaling of the lifetime in the mass, as expected from na\"ive semiclassical arguments for the probability of a tunneling phenomenon to occur.

https://arxiv.org/abs/1801.03353
Bohmian quantum gravity and cosmology
Nelson Pinto-Neto, Ward Struyve
(Submitted on 10 Jan 2018)
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.

https://arxiv.org/abs/1801.06017
Spin networks on adiabatic quantum computer
Jakub Mielczarek
(Submitted on 18 Jan 2018)
The article is addressing a possibility of implementation of spin network states on adiabatic quantum computer. The discussion is focused on application of currently available technologies and analyzes a concrete example of D-Wave machine. A class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor is introduced. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states, which may inspire development of new generations of adiabatic quantum computers. A possibility of simulating Loop Quantum Gravity is discussed and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed.

https://arxiv.org/abs/1801.07313
Towards Cosmological Dynamics from Loop Quantum Gravity
Bao-Fei Li, Parampreet Singh, Anzhong Wang
(Submitted on 22 Jan 2018 (v1), last revised 1 Feb 2018 (this version, v2))
We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC causing a non-singular bounce. Dynamics can be described by the Hamilton's or the Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one-to-one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the pre-bounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the post-bounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.

 

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https://arxiv.org/abs/1802.02382
Space and Time in Loop Quantum Gravity
Carlo Rovelli
(Submitted on 7 Feb 2018)
Quantum gravity is expected to require modifications of the notions of space and time. I discuss and clarify how this happens in Loop Quantum Gravity.

https://arxiv.org/abs/1802.02661
Gravitation in terms of observables
Rodolfo Gambini, Jorge Pullin
(Submitted on 7 Feb 2018)
In the 1960's, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program for gauge theories was completed for Yang--Mills theories by Gambini and Trias in the 1980's. Gauge theories could be understood as representations of certain group: the group of loops. The same formalism could not be implemented at that time for the gravitational case. Here we would like to propose an extension to the case of gravity. The resulting theory is described in terms of loops and open paths and can provide the underpinning for a new quantum representation for gravity distinct from the one used in loop quantum gravity or string theory. In it, space-time points are emergent entities that would only have quasi-classical status. The formulation may be given entirely in terms of Dirac observables that form a complete set of gauge invariant functions that completely define the Riemannian geometry of the spacetime. At the quantum level this formulation will lead to a reduced phase space quantization free of any constraints.

 

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https://arxiv.org/abs/1802.06251
Radial gauge fixing of first order gravity
Emanuele Alesci, Costantino Pacilio, Daniele Pranzetti
(Submitted on 17 Feb 2018)
We consider the first order connection formulation of 4D general relativity in the radial gauge. We show how the partial gauge fixing of the phase space canonical coordinates leads to the appearance of second class constraints in the theory. We employ the gauge unfixing procedure in order to successfully complete the Dirac treatment of the system. While equivalent to the inversion of the Dirac matrix, the gauge unfixing allows us to work directly with the reduced phase space and the ordinary Poisson bracket. At the same time, we explicitly derive the new set of residual first class constraints preserving the partial gauge fixing, which are linear combinations of the original constraints, and these turn out to contain nonlinear terms. While providing an explicit example of how to consistently recast general relativity in a given partial gauge, the main motivation of this classical analysis is the application of the Quantum Reduced Loop Gravity program to a Schwarzschild black hole geometry.

https://arxiv.org/abs/1802.07033
The constraint algebra in Smolins' G→0 limit of 4d Euclidean Gravity
Madhavan Varadarajan
(Submitted on 20 Feb 2018)
Smolin's generally covariant GNewton→0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in Loop Quantum Gravity. In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG like construction of non-trivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin's remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of 2 or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG like quantization of Paramaterized Field Theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states (b) yields anomaly free commutators between pairs of Hamiltonian constraints and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.

https://arxiv.org/abs/1802.09114
Loop Quantum Corrected Einstein Yang-Mills Black Holes
Mason Protter, Andrew DeBenedictis
(Submitted on 26 Feb 2018)
In this paper we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possesses both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian along with the restriction to homogeneity allows for an anomaly free effective quantization. In particular we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R×S2. Beyond the bounce the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.

https://arxiv.org/abs/1803.00332
Geometry Transition in Covariant Loop Quantum Gravity
Christodoulou Marios
(Submitted on 1 Mar 2018)
In this manuscript we present a calculation of a physical observable in a non-perturbative quantum gravitational physical process from covariant Loop Quantum Gravity. The process regards the transition of a trapped region to an anti--trapped region, treated as a quantum geometry transition akin to gravitational tunneling. Figuratively speaking, this is a quantum transition of a black hole to a white hole. The physical observables are the characteristic timescales in which the process takes place.
After an introduction, we begin with two chapters that review, define and extend main tools relevant to Lorentzian spinfoams and their semiclassical limit. We then dedicate a chapter to the classical exterior spacetime, which provides the setup for the problem. In the last two chapters, we arrive at an explicit, analytically well-defined and finite expression for a transition amplitude describing this process and use the semiclassical approximation to estimate the relevant amplitudes for an arbitrary choice of boundary conditions. We conclude that the transition is predicted to be allowed by LQG, with a characteristic duration that is linear in the mass, when the process takes place. The probability for the process to take place is exponentially suppressed but non-zero, resulting to a long lifetime.
Comments: PhD thesis submitted for the degree of Doctor in Theoretical and Mathematical Physics. Defended at the Center for Theoretical Physics/CNRS/Aix-Marseille University, the 23rd of October 2017. The manuscript is written in English and begins with a short summary in French

https://arxiv.org/abs/1803.01119
Effective line elements and black-hole models in canonical (loop) quantum gravity
Martin Bojowald, Suddhasattwa Brahma, Dong-han Yeom
(Submitted on 3 Mar 2018)
Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance in an effective Friedmann equation, but there should also be implications for a modified space-time structure. Quantum space-time effects, however, are often ignored in this setting because they are not obvious: they require a careful analysis of gauge transformations and the anomaly problem. It is shown here how modified space-time structures and effective line elements can be derived unambiguously, provided an off-shell anomaly-free system of modified constraints exists. The resulting effective line elements reveal signature change as an inescapable consequence of non-classical gauge transformations in the presence of holonomy modifications. The general framework is then specialized to black-hole models in loop quantum gravity. In contrast to previous studies, a self-consistent space-time structure is taken into account, leading to a new picture of black-hole interiors.

https://arxiv.org/abs/1803.01152
Loop quantum deformation of a Schwarzschild black hole: an effective metric
Jibril Ben Achour, Frédéric Lamy, Hongguang Liu, Karim Noui
(Submitted on 3 Mar 2018)
We consider the modified Einstein equations obtained in the framework of effective loop quantum gravity for spherically symmetric space-times. When one takes into account (only point-wise holonomy) quantum corrections, the deformation of Einstein equations is parametrized by a function f(x) of one variable . We solve explicitly these equations for static black holes and find the effective metric in the region inside the black hole for any f(x). When f(x) is the usual function used in loop quantum gravity, the effective metric presents strong similarities with the Reissner-Nordstrom metric (with a regular trapped region): it tends to the expected Schwarzschild metric when one approaches the outer horizon, and the inner horizon replaces the original Schwarzschild singularity. We discuss the possibility to extend the solution outside the trapped region, and possible phenomenological consequences of our results.

https://arxiv.org/abs/1803.02577
The Bronstein hypercube of quantum gravity
Daniele Oriti
(Submitted on 7 Mar 2018 (v1), last revised 8 Mar 2018 (this version, v2))
We argue for enlarging the traditional view of quantum gravity, based on "quantizing GR", to include explicitly the non-spatiotemporal nature of the fundamental building blocks suggested by several modern quantum gravity approaches (and some semi-classical arguments), and to focus more on the issue of the emergence of continuum spacetime and geometry from their collective dynamics. We also discuss some recent developments in quantum gravity research, aiming at realising these ideas, in the context of group field theory, random tensor models, simplicial quantum gravity, loop quantum gravity, spin foam models.

 

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https://arxiv.org/abs/1803.04374
Spacetime is as spacetime does
Vincent Lam, Christian Wuthrich
(Submitted on 12 Mar 2018)
Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must establish how relativistic spacetime emerges from their non-spatiotemporal structures. We argue that in order to secure this emergence, it is sufficient to establish that only those features of relativistic spacetimes functionally relevant in producing empirical evidence must be recovered. In order to complete this task, an account must be given of how the more fundamental structures instantiate these functional roles. We illustrate the general idea in the context of causal set theory and loop quantum gravity, two prominent approaches to quantum gravity.

https://arxiv.org/abs/1803.06963
Interpreting Theories without a Spacetime
Sebastian De Haro, Henk De Regt
(Submitted on 19 Mar 2018)
In this paper we have two aims: first, to draw attention to the close connexion between interpretation and scientific understanding; second, to give a detailed account of how theories without a spacetime can be interpreted, and so of how they can be understood.
In order to do so, we of course need an account of what is meant by a theory `without a spacetime': which we also provide in this paper.
We describe three tools, used by physicists, aimed at constructing interpretations which are adequate for the goal of understanding. We analyse examples from high-energy physics illustrating how physicists use these tools to construct interpretations and thereby attain understanding. The examples are: the 't Hooft approximation of gauge theories, random matrix models, causal sets, loop quantum gravity, and group field theory.

https://arxiv.org/abs/1803.09653
Mimetic Loop Quantum Cosmology
Jaume de Haro, Llibert Aresté Saló, Supriya Pan
(Submitted on 26 Mar 2018)
Considering as usual that the underlying geometry of our universe is well described by the spatially flat Friedmann-Lemaitre-Robertson-Walker line element, we show that the background of holonomy corrected Loop Quantum Cosmology (LQC) is equivalent to a simple modified version of the mimetic gravity. We also analyze the scalar and tensor perturbations of this modified mimetic model from which we find that, at the level of scalar perturbations, the modified mimetic model is exactly equivalent to the LQC while at the level of tensor perturbations, the modified mimetic gravity is indistinguishable from the General Relativity.

https://arxiv.org/abs/1803.10289
Emergence of Spacetime in a restricted Spin-foam model
Sebastian Steinhaus, Johannes Thürigen
(Submitted on 27 Mar 2018)
The spectral dimension has proven to be a very informative observable to understand the properties of quantum geometries in approaches to quantum gravity. In loop quantum gravity and its spin foam description, it has not been possible so far to calculate the spectral dimension of spacetime. As a first step towards this goal, here we determine the spacetime spectral dimension in the simplified spin foam model restricted to hypercuboids. Using Monte Carlo methods we compute the spectral dimension for state sums over periodic spin foam configurations on infinite lattices. For given periodicity, i.e. number of degrees of freedom, we find a range of scale where an intermediate spectral dimension between 0 and 4 can be found, continuously depending on the parameter of the model. Under an assumption on the statistical behaviour of the Laplacian we can explain these results analytically. This allows us to take the thermodynamic limit of large periodicity and find a phase transition from a regime of effectively 0-dimensional to 4-dimensional spacetime. At the point of phase transition, dynamics of the model are scale invariant which can be seen as restoration of diffeomorphism invariance of flat space. Considering the spectral dimension as an order parameter for renormalization we find a renormalization group flow to this point as well. Being the first instance of an emergence of 4-dimensional spacetime in a spin foam model, the properties responsible for this result seem to be rather generic. We thus expect similar results for more general, less restricted spin foam models.

 

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https://arxiv.org/abs/1803.10807
Hamiltonian structure and connection-dynamics of Weyl gravity
Qian Chen, Yongge Ma
(Submitted on 28 Mar 2018)
A crucial property of Weyl gravity is its conformal invariance. It is shown how this gauge symmetry is exactly reflected by the two constraints in the Hamiltonian framework. Since the spatial 3-metric is one of the configuration variables. The phase space of Weyl gravity can be extended to include internal gauge freedom by triad formalism. Moreover, by a canonical transformation, we obtain a new Hamiltonian formulation of Weyl gravity with an SU(2) connection as one of its configuration variables. This connection dynamical formalism lays a foundation to quantize Weyl gravity nonperturbatively by applying the method of loop quantum gravity.

https://arxiv.org/abs/1803.10858
Is the average of timelike singularities really spacelike?
Eugenio Bianchi, Hal M. Haggard
(Submitted on 28 Mar 2018)
Due to quantum fluctuations, a non-rotating black hole should be the average over an ensemble of black hole geometries with angular momentum. This observation invites the question: Is the average of timelike singularities really spacelike? We use the Bekenstein-Hawking entropy formula to introduce a microcanonical ensemble for spin fluctuations and argue that the onset of quantum gravity is always spacelike. We also hint at the possibility of an observational test.

https://arxiv.org/abs/1803.10809
Volume and Boundary Face Area of a Regular Tetrahedron in a Constant Curvature Space
Omar Nemoul, Noureddine Mebarki
(Submitted on 23 Mar 2018)
An example of the volume and boundary face area of a curved polyhedron for the case of regular spherical and hyperbolic tetrahedron is discussed. An exact formula is explicitly derived as a function of the scalar curvature and the edge length. This work can be used in loop quantum gravity and Regge calculus in the context of a non-vanishing cosmological constant.

https://arxiv.org/abs/1804.00012
Effective universality in quantum gravity
Astrid Eichhorn, Peter Labus, Jan M. Pawlowski, Manuel Reichert
(Submitted on 30 Mar 2018)
We investigate the asymptotic safety scenario for a scalar-gravity system. This system contains two avatars of the dynamical Newton coupling, a gravitational self-coupling and a scalar-graviton coupling. We uncover an effective universality for the dynamical Newton coupling on the quantum level: its momentum-dependent avatars are in remarkable quantitative agreement in the scaling regime of the UV fixed point. For the background Newton coupling, this effective universality is not present, but qualitative agreement remains.

https://arxiv.org/abs/1804.00960
Singularity from star collapse, torsion and asymptotic safety of gravity
Abhishek Majhi
(Submitted on 3 Apr 2018)
A star of mass greater than the Chandrasekhar limit is believed to undergo a gravitational collapse to form a singularity, owing to Hawking-Penrose singularity theorem which is based on the Raychaudhuri equation in the absence of torsion. We argue that the spin-aspect of matter can lead to the evasion of singularity, caused by its mass-aspect, via torsion in asymptotically safe gravity.

https://arxiv.org/abs/1804.01003
An area rescaling ansatz and black hole entropy from loop quantum gravity
Abhishek Majhi
(Submitted on 3 Apr 2018)
Considering the possibility of `renormalization' of the gravitational constant on the horizon, leading to a dependence on the level of the associated Chern-Simons theory, a rescaled area spectrum is proposed for the non-rotating black hole horizon in loop quantum gravity. The statistical mechanical calculation leading to the entropy provides a unique choice of the rescaling function for which the Bekenstein-Hawking area law is yielded without the need to choose the Barbero-Immirzi parameter (γ). γ is determined by studying the limit in which the `renormalized' gravitational constant on the horizon asymptotically approaches the `bare' value. Unlike the usual, much criticized, practice of choosing γ just for the sake of the entropy matching the area law, its value is now rather determined by a physical consistency requirement.

 

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https://arxiv.org/abs/1804.02184
The emergence of space and time
Christian Wuthrich
(Submitted on 6 Apr 2018)
Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set theory and loop quantum gravity. This would raise philosophical concerns regarding the empirical coherence and general adequacy of theories in quantum gravity. If it can be established, however, that spacetime emerges in the appropriate circumstances and how all its relevant aspects are explained in fundamental non-spatiotemporal terms, then the challenge is fully met. It is argued that a form of spacetime functionalism offers the most promising template for this project.

https://arxiv.org/abs/1804.02428
A predictive framework for quantum gravity and black hole to white hole transition
Robert Oeckl (CCM-UNAM)
(Submitted on 6 Apr 2018)
The apparent incompatibility between quantum theory and general relativity has long hampered efforts to find a quantum theory of gravity. The recently proposed positive formalism for quantum theory purports to remove this incompatibility. We showcase the power of the positive formalism by applying it to the black hole to white hole transition scenario that has been proposed as a possible effect of quantum gravity. We show how the characteristic observable of this scenario, the bounce time, can be predicted within the positive formalism, while a traditional S-matrix approach fails at this task. Our result also involves a conceptually novel use of positive operator valued measures.

https://arxiv.org/abs/1804.02262
Cosmological consequences of Quantum Gravity proposals
Marco de Cesare
(Submitted on 6 Apr 2018)
In this thesis, we study the implications of Quantum Gravity models for the dynamics of spacetime and the ensuing departures from classical General Relativity. The main focus is on cosmological applications, particularly the impact of quantum gravitational effects on the dynamics of a homogenous and isotropic cosmological background. Our interest lies in the consequences for the evolution of the early universe and singularity resolution, as well as in the possibility of providing an alternative explanation for dark matter and dark energy in the late universe.
The thesis is divided into two main parts, dedicated to alternative (and complementary) ways of tackling the problem of Quantum Gravity. The first part is concerned with cosmological applications of background independent approaches to Quantum Gravity, both in the context of loop quantisation and in quantum geometrodynamics. Particularly relevant in this work is the Group Field Theory approach, which we use to study the effective dynamics of the emergent universe from a full theory of Quantum Gravity (i.e. without symmetry reduction).
In the second part, modified gravity theories are introduced as tools to provide an effective description of quantum gravitational effects, e.g. by introducing new degrees of freedom and symmetries. Particularly relevant in this respect is local conformal invariance, which finds a natural realisation in the framework of Weyl geometry. We build a modified theory of gravity based on such symmetry principle, and argue that new fields in the extended gravitational sector may play the role of dark matter. New degrees of freedom are also natural in models with varying fundamental `constants', which we examine critically.
Finally, we discuss prospects for future work and point at directions for the derivation of realistic cosmological models from Quantum Gravity candidates.

https://arxiv.org/abs/1804.02560
Quantum gravity for piecewise flat spacetimes
Aleksandar Mikovic, Marko Vojinovic
(Submitted on 7 Apr 2018)
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental degrees of freedom are the edge lengths of the triangulation. One can work with finitely many edge lengths, so that the corresponding Regge path integral can be made finite by using an appropriate path-integral measure. The semi-classical limit is computed by using the effective action formalism, and the existence of a semi-classical effective action restricts the choice of the path-integral measure. The classical limit is given by the Regge action, so that one has a quantum gravity theory for a piecewise-flat general relativity. By using the effective action formalism we show that the observed value of the cosmological constant can be recovered from the effective cosmological constant. When the number of 4-simplices in the spacetime triangulation is large, then the PL effective action is well approximated by a quantum field theory effective action with a physical cutoff determined by the smallest edge length.

 

[atyy]

https://arxiv.org/abs/1804.00023
Renormalization in symmetry restricted spin foam models with curvature
Benjamin Bahr, Giovanni Rabuffo, Sebastian Steinhaus
(Submitted on 30 Mar 2018 (v1), last revised 17 Apr 2018 (this version, v2))
We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov (EPRL-FK) spin foam model in its asymptotic limit. The vertex amplitude is deformed to include a cosmological constant term. The state sum is reduced to describe a foliated spacetime whose spatial slices are flat, isotropic and homogeneous. The model admits a non-vanishing extrinsic curvature whereas the scale factor can expand or contract at successive time steps.
The reduction of degrees of freedom allows a numerical evaluation of certain geometric observables on coarser and finer discretizations. Their comparison defines the renormalization group (RG) flow of the model in the parameters (α,Λ,G). We first consider the projection of the RG flow along the α direction, which shows a UV-attractive fixed point. Then, we extend our analysis to two- and three-dimensional parameter spaces. Most notably, we find the indications of a fixed point in the (α,Λ,G) space showing one attractive and two repulsive directions.

https://arxiv.org/abs/1804.04147
White-hole dark matter and the origin of past low-entropy
Carlo Rovelli, Francesca Vidotto
(Submitted on 11 Apr 2018 (v1), last revised 21 Apr 2018 (this version, v2))
Recent results on the end of black hole evaporation give new weight to the hypothesis that a component of dark matter could be formed by remnants of evaporated black holes: stable Planck-size white holes with a large interior. The expected lifetime of these objects is consistent with their production at reheating. But remnants could also be pre-big bang relics in a bounce cosmology, and this possibility has strong implications on the issue of the source of past low entropy: it could realize a perspectival interpretation of past low entropy. The ideas briefly presented in this essay are developed in forthcoming papers.

https://arxiv.org/abs/1805.08257
Probing the Shape of Quantum Surfaces: the Quadrupole Moment Operator
Christophe Goeller, Etera R. Livine
(Submitted on 21 May 2018)
The standard toolkit of operators to probe quanta of geometry in loop quantum gravity consists in area and volume operators as well as holonomy operators. New operators have been defined, in the U(N) framework for intertwiners, which allow to explore the finer structure of quanta of geometry. However these operators do not carry information on the global shape of the intertwiners. Here we introduce dual multipole moments for continuous and discrete surfaces, defined through the normal vector to the surface, taking special care to maintain parametrization invariance. These are raised to multipole operators probing the shape of quantum surfaces. Further focusing on the quadrupole moment, we show that it appears as the Hessian matrix of the large spin Gaussian approximation of coherent intertwiners, which is the standard method for extracting the semi-classical regime of spinfoam transition amplitudes. This offers an improvement on the usual loop quantum gravity techniques, which mostly focus on the volume operator, in the perspective of modeling (quantum) gravitational waves as shape fluctuations waves propagating on spin network states.

https://arxiv.org/abs/1804.08643
Loop quantum gravity and the continuum
Wolfgang Wieland
(Submitted on 23 Apr 2018)
In this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum. We will argue, in particular, that in three spacetime dimensions the discrete spectra for the geometric boundary observables that we find in loop quantum gravity can be understood from the quantisation of a conformal boundary field theory in the continuum without ever introducing spin networks or triangulations of space. At a technical level, the starting point is the Hamiltonian formalism for general relativity in regions with boundaries at finite distance. At these finite boundaries, we choose specific Robin boundary conditions (the boundary is a minimal surface) that are derived from a boundary field theory for an SU(2) boundary spinor, which is minimally coupled to the spin connection in the bulk. The resulting boundary equations of motion define a conformal field theory with vanishing central charge. We will quantise this boundary field theory and show that the length of a one-dimensional cross section of the boundary has a discrete spectrum. In addition, we will introduce a new class of coherent states, study the quasi-local observables that generate the quasi-local Virasoro algebra and discuss some strategies to evaluate the partition function of the theory.

https://arxiv.org/abs/1805.08644
On the Hamiltonian operator in loop quantum gravity
Cong Zhang, Jerzy Lewandowski, Yongge Ma
(Submitted on 22 May 2018 (v1), last revised 23 May 2018 (this version, v2))
Although the physical Hamiltonian operator can be constructed in the deparameterized model of loop quantum gravity coupled to a scalar field, its property is still unknown. This open issue is attacked in this paper by considering an operator H^v representing the square of the physical Hamiltonian operator acting nontrivially on two-valent spin networks. The Hilbert space Hv preserved by the graphing changing operator H^v is consist of spin networks with a single two-valent non-degenerate vertex. The matrix element of H^v are explicitly worked out in a suitable basis. It turns out that the operator H^v is essentially self-adjoint, which implies a well-defined physical Hamiltonian operator in Hv for the deparameterized model.

https://arxiv.org/abs/1804.11101
The Tensor Track V: Holographic Tensors
Nicolas Delporte, Vincent Rivasseau
(Submitted on 30 Apr 2018)
We review the fast developing subject of tensor models for the NAdS2/NCFT1 holographic correspondence. We include a brief review of the Sachdev-Ye-Kitaev (SYK) model and then focus on the associated quantum mechanical tensor models (GW and CTKT). We examine their main features and how they compare with SYK. To end, we discuss different extensions: the large D limit of matrix-tensor models, the large N expansion of symmetric/antisymmetric tensors, the use of probes, the construction of a bilocal action for tensors, some attempts to extend the above models to higher dimensions and a proposal to break the tensor symmetry.

https://arxiv.org/abs/1805.01619
Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
Joseph Ben Geloun, Tim A. Koslowski, Daniele Oriti, Antonio D. Pereira
(Submitted on 4 May 2018)
In this paper we consider the complete momentum-independent quartic order truncation for the effective average action of a real Abelian rank 3 tensorial group field theory. This complete truncation includes non-melonic as well as double-trace interactions. In the usual functional renormalization group perspective, the inclusion of more operators that belong to the underlying theory space corresponds to an improvement of the truncation of the effective average action. We show that the inclusion of non-melonic and double-trace operators in the truncation brings subtleties. In particular, we discuss the assignment of scaling dimensions to the non-melonic sector and how the inclusion of double-trace operators considerably changes the results for critical exponents when they are not included. We argue that this is not a particular problem of the present model by comparing the results with a pure tensor model. We discuss how these issues should be investigated in future work.

https://arxiv.org/abs/1805.03099
The separate universe framework in group field theory condensate cosmology
Florian Gerhardt, Daniele Oriti, Edward Wilson-Ewing
(Submitted on 8 May 2018)
We use the separate universe framework to study cosmological perturbations within the group field theory formalism for quantum gravity, based on multi-condensate quantum states. Working with a group field theory action for gravity minimally coupled to four scalar fields that can act as a set of relational clock and rods, we argue that these multi-condensate states correspond to cosmological space-times with small long-wavelength scalar perturbations. Equations of motion for the cosmological perturbations are derived, which in the classical limit agree with the standard results of general relativity and also include quantum gravity corrections that become important when the space-time curvature approaches the Planck scale.

https://arxiv.org/abs/1805.03224
Pre-big-bang black-hole remnants and the past low entropy
Carlo Rovelli, Francesca Vidotto
(Submitted on 8 May 2018)
Dark matter could be composed by black-hole remnants formed before the big-bang era in a bouncing cosmology. This hypothetical scenario has major implications on the issue of the arrow of time: it would upset a common attribution of past low entropy to the state of the geometry, and provide a concrete realisation to the perspectival interpretation of past low entropy.

https://arxiv.org/abs/1805.03872
Small black/white hole stability and dark matter
Carlo Rovelli, Francesca Vidotto
(Submitted on 10 May 2018)
We show that the expected lifetime of white holes formed as remnants of evaporated black holes is consistent with their production at reheating. We give a simple quantum description of these objects and argue that a quantum superposition of black and white holes with large interiors is stable, because it is protected by the existence of a minimal eigenvalue of the area, predicted by Loop Quantum Gravity. These two results support the hypothesis that a component of dark matter could be formed by small black hole remnants.

https://arxiv.org/abs/1806.00456
Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
Clement Delcamp, Bianca Dittrich
(Submitted on 1 Jun 2018)
Using a recent strategy to encode the space of flat connections on a three-manifold with string-like defects into the space of flat connections on a so-called 2d Heegaard surface, we propose a novel way to define gauge invariant bases for (3+1)d lattice gauge theories and gauge models of topological phases. In particular, this method reconstructs the spin network basis and yields a novel dual spin network basis. While the spin network basis allows to interpret states in terms of electric excitations, on top of a vacuum sharply peaked on a vanishing electric field, the dual spin network basis describes magnetic (or curvature) excitations, on top of a vacuum sharply peaked on a vanishing magnetic field (or flat connection). This technique is also applicable for manifolds with boundaries. We distinguish in particular a dual pair of boundary conditions, namely of electric type and of magnetic type. This can be used to consider a generalization of Ocneanu's tube algebra in order to reveal the algebraic structure of the excitations associated with certain 3d manifolds.

https://arxiv.org/abs/1807.03066
Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recouping theory
Pietro Dona, Giorgio Sarno
(Submitted on 9 Jul 2018)
The intricated combinatorial structure and the non-compactness of the Lorentz group have always made the computation of SL(2,C) EPRL spin foam transition amplitudes a very hard and resource demanding task. With \texttt{sl2cfoam} we provide a C-coded library for the evaluation of the Lorentzian EPRL vertex amplitude. We provide a tool to compute the Lorentzian EPRL 4-simplex vertex amplitude in the intertwiner basis and some utilities to evaluate SU(2) invariants, booster functions and SL(2,C) Clebsch-Gordan coefficients. We discuss the data storage, parallelizations, time, and memory performances and possible future developments.

https://arxiv.org/abs/1807.03334
An introduction to the SYK model
Vladimir Rosenhaus
(Submitted on 9 Jul 2018)
These notes are a short introduction to the Sachdev-Ye-Kitaev model. We discuss: SYK and tensor models as a new class of large N quantum field theories, the near-conformal invariance in the infrared, the computation of correlation functions, generalizations of SYK, and applications to AdS/CFT and strange metals.

https://arxiv.org/abs/1807.02501
Tensor networks as path integral geometry
Ashley Milsted, Guifre Vidal
(Submitted on 6 Jul 2018)
In the context of a quantum critical spin chain whose low energy physics corresponds to a conformal field theory (CFT), it was recently demonstrated [A. Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks used for numerically describing the ground state of the spin chain can also be used to implement (discrete, approximate versions of) conformal transformations on the lattice. In the continuum, the same conformal transformations can be implemented through a CFT path integral on some curved spacetime. Based on this observation, in this paper we propose to interpret the tensor networks themselves as a path integrals on curved spacetime. This perspective assigns (a discrete, approximate version of) a geometry to the tensor network, namely that of the underlying curved spacetime.

 

[atyy]

https://arxiv.org/abs/1807.06098
Spin-foam model for gravity coupled to massless scalar field
Marcin Kisielowski, Jerzy Lewandowski
(Submitted on 16 Jul 2018)
A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.

https://arxiv.org/abs/1807.06354
Hamiltonian analysis of the BFCG formulation of General Relativity
Aleksandar Mikovic, Miguel A. Oliveira, Marko Vojinovic
(Submitted on 17 Jul 2018)
We perform the complete Hamiltonian analysis of the BFCG action for General Relativity. We determine all the constraints of the theory and classify them into the first-class and the second-class constraints. We also show how the canonical formulation of BFCG General Relativity reduces to the Einstein-Cartan and triad canonical formulations. The reduced phase space analysis also gives a 2-connection which is suitable for the construction of a spin-foam basis which will be a categorical generalization of the spin-network basis from Loop Quantum Gravity.

https://arxiv.org/abs/1807.06848
Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners
Etera R. Livine
(Submitted on 18 Jul 2018)
We describe the Lorentzian version of the Kapovitch-Millson phase space for polyhedra with N faces. Starting with the Schwinger representation of the su(1,1) Lie algebra in terms of a pair of complex variables (or spinor), we define the phase space for a space-like vectors in the three-dimensional Minkowski space R1,2. Considering N copies of this space, quotiented by a closure constraint forcing the sum of those 3-vectors to vanish, we obtain the phase space for Lorentzian polyhedra with N faces whose normal vectors are space-like, up to Lorentz transformations. We identify a generating set of SU(1,1)-invariant observables, whose flow by the Poisson bracket generate both area-preserving and area-changing deformations. We further show that the area-preserving observables form a glN(R) Lie algebra and that they generate a GLN(R) action on Lorentzian polyhedra at fixed total area. That action is cyclic and all Lorentzian polyhedra can be obtained from a totally squashed polyhedron (with only two non-trivial faces) by a GLN(R) transformation. All those features carry on to the quantum level, where quantum Lorentzian polyhedra are defined as SU(1,1) intertwiners between unitary SU(1,1)-representations from the principal continuous series. Those SU(1,1)-intertwiners are the building blocks of spin network states in loop quantum gravity in 3+1 dimensions for time-like slicing and the present analysis applies to deformations of the quantum geometry of time-like boundaries in quantum gravity, which is especially relevant to the study of quasi-local observables and holographic duality.

https://arxiv.org/abs/1807.10704
Gravitational Fluctuations as an Alternative to Inflation
Herbert W. Hamber, Lu Heng Sunny Yu
(Submitted on 27 Jul 2018)
In this work we explore an explanation for the galaxy power spectrum P(k) based on the non-perturbative quantum field-theoretical treatment of Einstein gravity, instead of one based on inflation models. In particular the power spectral index, which represents the slope on the P(k) graph, can be related to critical scaling exponents derived from the Wilson renormalization group analysis, and one finds that the derived value fits favorably with the Sloan Digital Sky Survey telescope data. We then make use of the transfer functions, based only on the Boltzmann equations which describe states out of equilibrium, and Einstein's General Relativity, to extrapolate the power spectrum to the Cosmic Microwave Background (CMB) regime and find that the results fits rather well with current data. Our approach contrasts with the conventional explanation which uses inflation to generate the scale invariant Harrison-Zel'dovich spectrum on CMB scales, and uses the transfer function to extrapolate it to galaxy regime. The results we present here only assumes quantum field theory and Einstein's Gravity, and hence provides a competing explanation of the power spectrum, without relying on the assumptions usually associated with inflationary models.

https://arxiv.org/abs/1808.00207
Quantum fields in the background spacetime of a loop quantum gravity black hole
Flora Moulin, Killian Martineau, Julien Grain, Aurélien Barrau
(Submitted on 1 Aug 2018)
The description of black holes in loop quantum gravity is a hard and tricky task. In this article, we focus on a minisuperspace approach based on a polymerization procedure. We consider the resulting effective metric and study the propagation of quantum fields in this background. The cross sections for scalar particles and fermions are explicitly calculated. The radial equation of motion is also derived in full generality, beyond the specifically considered metric.

https://arxiv.org/abs/1808.00673
From Euclidean to Lorentzian Loop Quantum Gravity via a Positive Complexifier
Madhavan Varadarajan
(Submitted on 2 Aug 2018 (v1), last revised 5 Aug 2018 (this version, v2))
We construct a positive complexifier, differentiable almost everywhere on the classical phase space of real triads and SU(2) connections, which generates a Wick Transform from Euclidean to Lorentzian gravity everywhere except on a phase space set of measure zero. This Wick transform assigns an equal role to the self dual and anti-self dual Ashtekar variables in quantum theory. We argue that the appropriate quantum arena for an analysis of the properties of the Wick rotation is the diffeomorphism invariant Hilbert space of Loop Quantum Gravity (LQG) rather than its kinematic Hilbert space. We examine issues related to the construction, in quantum theory, of the positive complexifier as a positive operator on this diffeomorphism invariant Hilbert space. Assuming the existence of such an operator, we explore the possibility of identifying physical states in Lorentzian LQG as Wick rotated images of physical states in the Euclidean theory. Our considerations derive from Thiemann's remarkable proposal to define Lorentzian LQG from Euclidean LQG via the implementation in quantum theory of a phase space `Wick rotation' which maps real Ashtekar-Barbero variables to Ashtekar's complex, self dual variables.

https://arxiv.org/abs/1808.01252
A review on Loop Quantum Gravity
Pablo Antonio Moreno Casares
(Submitted on 3 Aug 2018)
The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for the theory: the canonical quantization (first two chapters) and spin foams (third). The final chapter will be devoted to studying some of the problems of the theory and what things remain to be developed. In chapter 3 we will also include an example of a simple calculation done in the frame of LQG: Schwarzschild black hole entropy.

https://arxiv.org/abs/1808.01744
The no-boundary wave function for loop quantum cosmology
Suddhasattwa Brahma, Dong-han Yeom
(Submitted on 6 Aug 2018)
Proposing smooth initial conditions is one of the most important tasks in quantum cosmology. On the other hand, the low-energy effective action, appearing in the semiclassical path integral, can get nontrivial quantum corrections near classical singularities due to specific quantum gravity proposals. In this article, we combine the well-known no-boundary proposal for the wavefunction of the universe with quantum modifications coming from loop quantum cosmology (LQC). Remarkably, we find that the restriction of a `slow-roll' type potential in the original Hartle-Hawking proposal is considerably relaxed due to quantum geometry regularizations. Interestingly, the same effects responsible for singularity-resolution in LQC also end up expanding the allowed space of smooth initial conditions leading to an inflationary universe.

 

[julian]

https://arxiv.org/abs/1808.00535
Pure states statistical mechanics: On its foundations and applications to quantum gravity
Fabio Anza
(Submitted on 1 Aug 2018)
The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in isolated quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study some equilibrium properties of many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Second, I exploited the "Concentration of Measure" phenomenon to study the macroscopic properties of the basis states of Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon, at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why a classical horizon exhibits thermal properties.

https://arxiv.org/abs/1808.03472
Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
Ademola Adeifeoba, Astrid Eichhorn, Alessia Platania
(Submitted on 10 Aug 2018)
We explore the fate of the curvature singularity of Schwarzschild (deSitter) black holes in asymptotically safe quantum gravity. Specifically, we upgrade the classical spacetime by including the running of the Newton coupling and cosmological constant. In this setting, the antiscreening character of the gravitational interaction can remove the singularity, yet a nonzero value of the cosmological constant in the ultraviolet appears to reintroduce it. We find hints that a finite value of the cosmological constant in the infrared is compatible with singularity resolution provided that the cosmological constant is driven to zero fast enough in the ultraviolet. We compare the corresponding bounds on the critical exponents to the literature.

https://arxiv.org/abs/1808.05842
On the possibility of laboratory evidence for quantum superposition of geometries
Marios Christodoulou, Carlo Rovelli
(Submitted on 17 Aug 2018)
We analyze the recent proposal of measuring a quantum gravity phenomenon in the lab by entangling two particles gravitationally. We give a generally covariant description of this phenomenon, where the relevant effect turns out to be a quantum superposition of proper times. We point out that measurement of this effect would count as evidence for quantum superposition of spacetime geometries. This interpretation addresses objections appeared in the literature. We observe that the effect sheds light on the Planck mass, and argue that it is very plausibly a real effect.

https://arxiv.org/abs/1808.06974
Detailed background dynamics and trans-planckian effects in loop quantum cosmology
Killian Martineau
(Submitted on 21 Aug 2018)
Cosmology appears as the most promising way to test and constrain quantum gravity theories. Loop quantum gravity is among the most advanced attempts to perform a non-perturbative quantization of general relativity. Its cosmological counterpart, loop quantum cosmology, has clear predictions both for the cosmological background and for the perturbations. In particular, the initial Big Bang singularity is replaced by a bounce due to quantum geometry effects. In this proceeding I will focus on new results obtained in loop quantum cosmology: i) the prediction of the duration of inflation as a function of all the unknown parameters of the model and ii) new primordial power spectra obtained with modified dispersion relations accounting for trans-planckian effects.

https://arxiv.org/abs/1808.08857
A status report on the phenomenology of black holes in loop quantum gravity: Evaporation, tunneling to white holes, dark matter and gravitational waves
Aurélien Barrau, Killian Martineau, Flora Moulin
(Submitted on 27 Aug 2018)
The understanding of black holes in loop quantum gravity is becoming increasingly accurate. This review focuses on the possible experimental or observational consequences of the underlying spinfoam structure of space-time. It adresses both the aspects associated with the Hawking evaporation and the ones due to the possible existence of a bounce. Finally, consequences for dark matter and gravitational waves are considered.

https://arxiv.org/abs/1808.09216
Abelian 2+1D Loop Quantum Gravity Coupled to a Scalar Field
Christoph Charles
(Submitted on 28 Aug 2018)
In order to study 3d loop quantum gravity coupled to matter, we consider a simplified model of abelian quantum gravity, the so-called U(1)^3 model. Abelian gravity coupled to a scalar field shares a lot of commonalities with parameterized field theories. We use this to develop an exact quantization of the model. This is used to discuss solutions to various problems that plague even the 4d theory, namely the definition of an inverse metric and the role of the choice of representation for the holonomy-flux algebra.

https://arxiv.org/abs/1808.09765
Phase transitions in group field theory: The Landau perspective
Andreas G. A. Pithis, Johannes Thürigen
(Submitted on 29 Aug 2018)
In various approaches to quantum gravity continuum spacetime is expected to emerge from discrete geometries through a phase transition. In group field theory, various indications for such a transition have recently been found but a complete understanding of such a phenomenon remains an open issue. In this work, we investigate the critical behavior of different group field theory models in the Gaussian approximation. Applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation breaks down in the case of three-dimensional Euclidean quantum gravity as described by the dynamical Boulatov model on the compact group SU(2). This result is independent of the peculiar gauge symmetry and specific form of nonlocality of the model. On the contrary, we find that the Gaussian approximation is valid for a rank-1 GFT on the noncompact sector of fields on SL(2,R) related to Lorentzian models. Though a nonperturbative analysis is needed to settle the question of phase transitions for compact groups, the results may also indicate the necessity to consider group field theory on noncompact domains for phase transitions to occur.

https://arxiv.org/abs/1808.09971
Volume of 4-polytopes from bivectors
Benjamin Bahr
(Submitted on 29 Aug 2018)
In this article we prove a formula for the volume of 4-dimensional polytopes, in terms of their face bivectors, and the crossings within their boundary graph. This proves that the volume is an invariant of bivector-coloured graphs in $S^3$.

https://arxiv.org/abs/1808.10225
Phenomenology of Quantum Reduced Loop Gravity in the isotropic cosmological sector
Emanuele Alesci, Aurélien Barrau, Gioele Botta, Killian Martineau, Gabriele Stagno
(Submitted on 30 Aug 2018)
Quantum reduced loop gravity is designed to consistently study symmetry reduced systems within the loop quantum gravity framework. In particular, it bridges the gap between the effective cosmological models of loop quantum cosmology and the full theory, addressing the dynamics before the minisuperspace reduction. This mostly preserves the graph structure and SU(2) quantum numbers. In this article, we study the phenomenological consequences of the isotropic sector of the theory, the so-called emergent bouncing universe model. In particular, the parameter space is scanned and we show that the number of inflationary e-folds is almost always higher than the observational lower-bound. We also compute the primordial tensor power spectrum and study its sensitivity upon the fundamental parameters used in the model.

https://arxiv.org/abs/1808.10469
Group field theory and its cosmology in a matter reference frame
Steffen Gielen
(Submitted on 30 Aug 2018 (v1), last revised 25 Sep 2018 (this version, v2))
While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where coordinates are not a priori available and need to be reconstructed from physical degrees of freedom. We review the general idea of coupling free scalar fields to gravity and using these scalars as a "matter reference frame." The resulting coordinate system is harmonic, i.e. it satisfies harmonic (de Donder) gauge. We then show how to introduce such matter reference frames in the group field theory approach to quantum gravity, where spacetime is emergent from a "condensate" of fundamental quantum degrees of freedom of geometry, and how to use matter coordinates to extract physics. We review recent results in homogeneous and inhomogeneous cosmology, and give a new application to the case of spherical symmetry. We find tentative evidence that spherically symmetric group field theory condensates defined in this setting can reproduce the near-horizon geometry of a Schwarzschild black hole.

https://arxiv.org/abs/1809.00313
Cosmological perturbations with inverse-volume corrections in loop quantum cosmology
Yu Han
(Submitted on 2 Sep 2018)
Although the cosmological perturbations with inverse-volume corrections from loop quantum cosmology have been studied using the anomaly free algebra approach in many literatures, there still remains an important issue that some counter terms in the perturbed constraints cannot be uniquely fixed on the spatially flat FRW background, which causes ambiguities in the perturbation equations. In this paper we show that this problem can be overcome by extending the anomaly free algebra to spatially closed FRW background. We find that a consistent deformed algebra can be obtained in the spatially closed case, and each counter term can be uniquely fixed in terms of the inverse-volume correction functions, then by taking the large $r_o$ limit, we recover the anomaly free Hamiltonian on the spatially flat background, using this Hamiltonian we obtain the gauge invariant cosmological perturbations for scalar, vector and tensor modes in the spatially flat case. Moreover, we also derive the quantum corrected Mukhanov equations, from which the scalar and tensor spectral indices with inverse-volume corrections are given. The results obtained in this paper show some differences with those in previous literatures.

https://arxiv.org/abs/1809.00556
A change of perspective: switching quantum reference frames via a perspective-neutral framework
Augustin Vanrietvelde, Philipp A Hoehn, Flaminia Giacomini, Esteban Castro-Ruiz
(Submitted on 3 Sep 2018)
Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspective-neutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of arXiv:1712.07207, embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories as perspective-neutral and perspectival quantum theories, respectively. In this light, we suggest a new take on the relation between a `quantum general covariance' and the diffeomorphism symmetry in quantum gravity.

https://arxiv.org/abs/1809.00913
Observation of thermal Hawking radiation at the Hawking temperature in an analogue black hole
Juan Ramón Muñoz de Nova, Katrine Golubkov, Victor I. Kolobov, Jeff Steinhauer
(Submitted on 4 Sep 2018 (v1), last revised 14 Sep 2018 (this version, v2))
We measure the correlation spectrum of the Hawking radiation emitted by an analogue black hole and find it to be thermal at the Hawking temperature implied by the analogue surface gravity. The Hawking radiation is in the regime of linear dispersion, in analogy with a real black hole. Furthermore, the radiation inside of the black hole is seen to be composed of negative-energy partners only. This work confirms the prediction of Hawking's theory regarding the value of the Hawking temperature, as well as the thermality of the spectrum. The thermality of Hawking radiation is the root of the information paradox. The correlations between the Hawking and partner particles imply that the analogue black hole has no analogue firewall.

https://arxiv.org/abs/1809.01747
Glimpses of Space-Time Beyond the Singularities Using Supercomputers
Parampreet Singh
(Submitted on 5 Sep 2018)
A fundamental problem of Einstein's theory of classical general relativity is the existence of singularities such as the big bang. All known laws of physics end at these boundaries of classical space-time. Thanks to recent developments in quantum gravity, supercomputers are now playing an important role in understanding the resolution of big bang and black hole singularities. Using supercomputers, explorations of the very genesis of space and time from quantum geometry are revealing a novel picture of what lies beyond classical singularities and the new physics of the birth of our universe.

https://arxiv.org/abs/1809.01908
A Local Resolution of the Problem of Time
Edward Anderson
(Submitted on 6 Sep 2018 (v1), last revised 24 Sep 2018 (this version, v2))
We here announce and outline a solution of this major and longstanding foundational problem, dealing with all seven of its heavily-interrelated local facets.

 

[julian]

https://arxiv.org/abs/1809.03172
Non-adiabatic Evolution of Primordial Perturbations and non-Gaussinity in Hybrid Approach of Loop Quantum Cosmology
Qiang Wu, Tao Zhu, Anzhong Wang
(Submitted on 10 Sep 2018)
While loop quantum cosmology (LQC) predicts a robust quantum bounce of the background evolution of a Friedmann-Robertson-Walker (FRW) spacetime prior to the standard slow-roll inflation, whereby the big bang singularity is resolved, there are several different quantization procedures to cosmological perturbations, for instance, {\em the deformed algebra, dressed metric, and hybrid quantizations}. This paper devotes to study the quantum bounce effects of primordial perturbations in the hybrid approach. The main discrepancy of this approach is the effective positive mass at the quantum bounce for the evolution of the background that is dominated by the kinetic energy of the inflaton field at the bounce, while this mass is always nonpositive in the dressed metric approach. It is this positivity of the effective mass that violates the adiabatic evolution of primordial perturbations at the initial moments of the quantum bounce. With the assumption that the evolution of the background is dominated by the kinetic energy of the inflaton at the bounce, we find that the effective potentials for both scalar and tensor perturbations can be well approximately described by a P\"{o}schl-Teller (PT) potential, which allows us to find analytical solutions of perturbations, and from these analytical expressions we are able to study the non-adiabatic evolution of primordial perturbations in details. In particular, we derive their quantum bounce effects and investigate their observational constraints. In addition, the impacts of quantum bounce effects on the non-Gaussinity and their implication on the explanations of observed power asymmetry in CMB have also been explored.

https://arxiv.org/abs/1809.03884
Perturbations in Hybrid Loop Quantum Cosmology: Continuum Limit in Fourier Space
Beatriz Elizaga Navascués, Guillermo A. Mena Marugán
(Submitted on 11 Sep 2018)
We analyze the passage to a continuum limit of the mode spectrum of primordial perturbations around flat cosmological spacetimes in hybrid Loop Quantum Cosmology, showing that this limit can be reached even if one starts by considering a finite fiducial cell as spatial slice. We focus our attention on regimes in which the background cosmology follows the effective dynamics of Loop Quantum Cosmology, although we comment on extensions of our arguments beyond this regime, as well as to some formalisms other than the hybrid approach. Whereas the perturbed system can be described in an invariant way under changes of the fiducial volume using the standard variables of the improved prescription for Loop Quantum Cosmology, we show that the desired continuum limit can be established by means of scaling transformations of the physical volume when this volume grows unboundedly. These transformations lead to a model with a continuum of modes and independent of any scale of reference for the physical volume. For the sake of comparison, we also consider an alternative road to the continuum in Fourier space that has been employed in geometrodynamics and is based on the use of scaling transformations of the fiducial volume, together with variables that are independent of them.

https://arxiv.org/abs/1809.04465
Anomaly freedom in perturbative models of Euclidean loop quantum gravity
Jian-Pin Wu, Martin Bojowald, Yongge Ma
(Submitted on 12 Sep 2018)
Euclidean gravity provides an interesting test system for an analysis of cosmological perturbations in an effective Hamiltonian constraint with holonomy modifications from loop quantum gravity. This paper presents a discussion of scalar modes, with a specific form of the holonomy modification function derived from a general expansion in a connection formulation. Compared with some previous models, the constraint brackets are deformed in a different and more restricted way. A general comparison of anomaly-free brackets in various effective and operator versions shows overall consistency between different approaches.

https://arxiv.org/abs/1809.05093
Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
Augustin Vanrietvelde, Philipp A Hoehn, Flaminia Giacomini
(Submitted on 13 Sep 2018)
Given the importance of quantum reference systems to both quantum and gravitational physics, it is pertinent to develop a systematic method for switching between the descriptions of physics relative to different choices of quantum reference systems, which is valid in both fields. Here, we continue with such a unifying approach, begun in arxiv:1809.00556, whose key ingredients is a gravity-inspired symmetry principle, which enforces physics to be relational and leads, thanks to gauge related redundancies, to a perspective-neutral structure which contains all frame choices at once and via which frame perspectives can be consistently switched. Formulated in the language of constrained systems, the perspective-neutral structure turns out to be the constraint surface classically and the gauge invariant Hilbert space in the Dirac quantized theory. By contrast, a perspective relative to a specific frame corresponds to a gauge choice and the associated reduced phase and Hilbert space. Quantum reference frame switches thereby amount to a symmetry transformation. In the quantum theory, they require a transformation that takes one from the Dirac to a reduced quantum theory and we show that it amounts to a trivialization of the constraints and a subsequent projection onto the classical gauge fixing conditions. We illustrate this method in the relational N-body problem with rotational and translational symmetry. This model is particularly interesting because it features the Gribov problem so that globally valid gauge fixing conditions are impossible which, in turn, implies also that globally valid relational frame perspectives are absent in both the classical and quantum theory. These challenges notwithstanding, we exhibit how one can systematically construct the quantum reference frame transformations for the three-body problem.

https://arxiv.org/abs/1809.08083
Time in quantum theory, the Wheeler-DeWitt equation and the Born-Oppenheimer approximation
Alexander Yu. Kamenshchik, Alessandro Tronconi, Tereza Vardanyan, Giovanni Venturi
(Submitted on 21 Sep 2018)
We compare two different approaches to the treatment of the Wheeler-DeWitt equation and the introduction of time in quantum cosmology. One approach is based on the gauge-fixing procedure in theories with first-class constraints, while the other uses the Born-Oppenheimer method. We apply both to a very simple cosmological model and observe that they give similar predictions. We also discuss the problem of time in non-relativistic quantum mechanics and some questions concerning the correspondence between classical and quantum theories.

https://arxiv.org/abs/1809.08277
Hiding the cosmological constant
S. Carlip
(Submitted on 21 Sep 2018)
Perhaps the expectations of quantum field theory are right, and the universe really does have a very large cosmological constant. I show that if one does not assume homogeneity or an arrow of time at the Planck scale, a large class of initial data for general relativity exhibits expansions and shears that are enormous at small scales, but quickly average to zero macroscopically. For an infinite subset of this data, the averaged spatial curvature is also small, and has a vanishing time derivative. Subsequent evolution is more complex, but I argue that quantum fluctuations should preserve these properties. The resulting picture is a version of Wheeler's "spacetime foam," in which the cosmological constant produces high curvature at the Planck scale but is hidden at observable scales.

https://arxiv.org/abs/1809.09659
A quantum gravity extension to the Mixmaster dynamics
Edward Wilson-Ewing
(Submitted on 25 Sep 2018)
In the loop quantum cosmology effective dynamics for the vacuum Bianchi type I and type IX space-times, a non-singular bounce replaces the classical singularity. The bounce can be approximated as an instantaneous transition between two classical vacuum Bianchi I solutions, with simple transition rules relating the solutions before and after the bounce: the evolution of the mean logarithmic scale factor is reversed, while the shape parameters are unaffected. As a result, the loop quantum cosmology effective dynamics for the vacuum Bianchi IX space-time can be approximated by a sequence of classical vacuum Bianchi I solutions, following the usual Mixmaster transition maps in the classical regime, and undergoing a bounce with this new transition rule in the Planck regime.

https://arxiv.org/abs/1809.09874
The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology
Beatriz Elizaga Navascués, Daniel Martín de Blas, Guillermo A. Mena Marugán
(Submitted on 26 Sep 2018)
We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic states of low order and the non-oscillating vacuum introduced by Mart\'in de Blas and Olmedo, all imposed at the bounce. The adiabatic spectra are typically suppressed at large scales, and display rapid oscillations with an increase of power at intermediate scales. In the non-oscillating vacuum, there is power suppression for large scales, but the rapid oscillations are absent. We argue that the oscillations are due to the imposition of initial adiabatic conditions in the region of kinetic dominance, and that they would also be present in General Relativity. Finally, we discuss the sensitivity of our results to changes of the initial time and other data of the model.

https://arxiv.org/abs/1810.00949
On the Empirical Consequences of the AdS/CFT Duality
Radin Dardashti, Richard Dawid, Sean Gryb, Karim Thébault
(Submitted on 27 Sep 2018)
We provide an analysis of the empirical consequences of the AdS/CFT duality with reference to the application of the duality in a fundamental theory, effective theory and instrumental context. Analysis of the first two contexts is intended to serve as a guide to the potential empirical and ontological status of gauge/gravity dualities as descriptions of actual physics at the Planck scale. The third context is directly connected to the use of AdS/CFT to describe real quark-gluon plasmas. In the latter context, we find that neither of the two duals are confirmed by the empirical data.

https://arxiv.org/abs/1810.00238
The BKL scenario, infrared renormalization, and quantum cosmology
Martin Bojowald
(Submitted on 29 Sep 2018)
A discussion of inhomogeneity is indispensable to understand quantum cosmology, even if one uses the dynamics of homogeneous geometries as a first approximation. While a full quantization of inhomogeneous gravity is not available, a broad framework of effective field theory provides important ingredients for quantum cosmology. Such a setting also allows one to take into account lessons from the Belinski-Khalatnikov-Lifshitz (BKL) scenario. Based on several new ingredients, this article presents conditions on various parameters and mathematical constructions that appear in minisuperspace models. Examples from different approaches demonstrate their restrictive nature.

https://arxiv.org/abs/1810.01259
A relational Hamiltonian for group field theory
Edward Wilson-Ewing
(Submitted on 2 Oct 2018)
Using a massless scalar field as a clock variable, the Legendre transform of the group field theory Lagrangian gives a relational Hamiltonian. In the classical theory, it is natural to define 'equal relational time' Poisson brackets, where 'equal time' corresponds to equal values of the scalar field clock. The quantum theory can then be defined by imposing 'equal relational time' commutation relations for the fundamental operators of the theory, with the states being elements of a Fock space with their evolution determined by the relational Hamiltonian operator. A particularly interesting family of states are condensates, as they are expected to correspond to the cosmological sector of group field theory. For the relational Hamiltonian considered in this paper, the coarse-grained dynamics of a simple type of condensate states agree exactly with the Friedmann equations in the classical limit, and also include quantum gravity corrections that ensure the big-bang singularity is replaced by a bounce.

https://arxiv.org/abs/1810.01671
Cosmological Implications of the Bekenstein Bound
Tom Banks, Willy Fischler
(Submitted on 3 Oct 2018 (v1), last revised 9 Oct 2018 (this version, v2))
A brief review of "Holographic Space-Time" in the light of the seminal contributions of Jacob Bekenstein.

https://arxiv.org/abs/1810.01880
Black hole entropy and the Bekenstein bound
Raphael Bousso
(Submitted on 3 Oct 2018)
I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. I summarize a number of fascinating recent developments that grew out of Bekenstein's pioneering contributions, from the Ryu-Takayanagi proposal to the Quantum Null Energy Condition.

https://arxiv.org/abs/1810.02828
How perturbative is quantum gravity?
Astrid Eichhorn, Stefan Lippoldt, Jan M. Pawlowski, Manuel Reichert, Marc Schiffer
(Submitted on 5 Oct 2018)
We explore asymptotic safety of gravity-matter systems, discovering indications for a near-perturbative nature of these systems in the ultraviolet. Our results are based on the dynamical emergence of effective universality at the asymptotically safe fixed point. Our findings support the conjecture that an asymptotically safe completion of the Standard Model with gravity could be realized in a near-perturbative setting.

https://arxiv.org/abs/1810.04153
How to switch between relational quantum clocks
Philipp A Hoehn, Augustin Vanrietvelde
(Submitted on 9 Oct 2018)
Every clock is a physical system and thereby ultimately quantum. A naturally arising question is thus how to describe time evolution relative to quantum clocks and, specifically, how the dynamics relative to different quantum clocks are related. This is a particularly pressing issue in view of the multiple choice facet of the problem of time in quantum gravity, which posits that there is no distinguished choice of internal clock in generic general relativistic systems and that different choices lead to inequivalent quantum theories. Exploiting a recent unifying approach to switching quantum reference systems (arXiv:1809.00556, arXiv:1809:05093), we exhibit a systematic method for switching between different clock choices in the quantum theory. We illustrate it by means of the parametrized particle, which, like gravity, features a Hamiltonian constraint. We explicitly switch between the quantum evolution relative to the non-relativistic time variable and that relative to the particle's position, which requires carefully regularizing the zero-modes in the so-called time-of-arrival observable. While this toy model is simple, our approach is general and, in particular, directly amenable to quantum cosmology. It proceeds by systematically linking the reduced quantum theories relative to different clock choices via the clock-choice-neutral Dirac quantized theory, in analogy to coordinate changes on a manifold. This method overcomes the multiple choice problem here, showing that it is actually a multiple choice feature of the complete relational quantum theory, taken as the conjunction of Dirac and reduced quantized theories. Precisely this conjunction permits to consistently switch between different temporal reference systems, which is a prerequisite for a quantum notion of general covariance.

 

[*now*]

https://arxiv.org/abs/1802.04264
White Holes as Remnants: A Surprising Scenario for the End of a Black Hole
Eugenio Bianchi, Marios Christodoulou, Fabio D'Ambrosio, Hal M. Haggard, Carlo Rovelli
(Submitted on 12 Feb 2018 (v1), last revised 17 Mar 2018 (this version, v2))
Quantum tunneling of a black hole into a white hole provides a model for the full life cycle of a black hole. The white hole acts as a long-lived remnant, solving the black-hole information paradox. The remnant solution of the paradox has long been viewed with suspicion, mostly because remnants seemed to be such exotic objects. We point out that (i) established physics includes objects with precisely the required properties for remnants: white holes with small masses but large finite interiors; (ii) non-perturbative quantum-gravity indicates that a black hole tunnels precisely into such a white hole, at the end of its evaporation. We address the objections to the existence of white-hole remnants, discuss their stability, and show how the notions of entropy relevant in this context allow them to evade several no-go arguments. A black hole's formation, evaporation, tunneling to a white hole, and final slow decay, form a unitary process that does not violate any known physics.

https://arxiv.org/abs/1811.00532
Statistical equilibrium of tetrahedra from maximum entropy principle
Goffredo Chirco, Isha Kotecha, Daniele Oriti
(Submitted on 1 Nov 2018)
Discrete formulations of (quantum) gravity in four spacetime dimensions build space out of tetrahedra. We investigate a statistical mechanical system of tetrahedra from a many-body point of view based on non-local, combinatorial gluing constraints that are modeled as multi-particle interactions. We focus on Gibbs equilibrium states, constructed using Jaynes' principle of constrained maximisation of entropy, which has been shown recently to play an important role in characterising equilibrium in background independent systems. We apply this principle first to classical systems of many tetrahedra using different examples of geometrically motivated constraints. Then for a system of quantum tetrahedra, we show that the quantum statistical partition function of a Gibbs state with respect to some constraint operator can be reinterpreted as a partition function for a quantum field theory of tetrahedra, taking the form of a group field theory.

https://arxiv.org/abs/1811.03667
Light Cone Black Holes
Tommaso De Lorenzo, Alejandro Perez
(Submitted on 8 Nov 2018)
When probed with conformally invariant matter fields, light cones in Minkowski spacetime satisfy thermodynamical relations which are the analog of those satisfied by stationary black holes coupled to standard matter fields. These properties stem from the fact that light cones are conformal Killing horizons stationary with respect to observers following the radial conformal Killing fields in flat spacetime. The four laws of light cone thermodynamics relate notions such as (conformal) temperature, (conformal) surface gravity, (conformal) energy and a conformally invariant notion related to area change. These quantities do not admit a direct physical interpretation in flat spacetime. However, they become the usual thermodynamical quantities when Minkowski is mapped, via a Weyl transformation, to a target spacetime where the conformal Killing field becomes a proper Killing field. In this paper we study the properties of such spacetimes. The simplest realisation turns out to be the Bertotti-Robinson solution, which is known to encode the near horizon geometry of near extremal and extremal charged black holes. The analogy between light cones in flat space and black hole horizons is therefore strengthened. The construction works in arbitrary dimensions; in two dimensions one recovers the Jackiv-Teitelboim black hole of dilaton gravity. Other interesting realisations are also presented.

https://arxiv.org/abs/1811.08007
Quantum insights on Primordial Black Holes as Dark Matter
Francesca Vidotto
(Submitted on 19 Nov 2018)
A recent understanding on how quantum effects may affect black-hole evolution opens new scenarios for dark matter, in connection with the presence of black holes in the very early universe. Quantum fluctuations of the geometry allow for black holes to decay into white holes via a tunnelling. This process yields to an explosion and possibly to a long remnant phase, that cures the information paradox. Primordial black holes undergoing this evolution constitute a peculiar kind of decaying dark matter, whose lifetime depends on their mass M and can be as short as M2. As smaller black holes explode earlier, the resulting signal have a peculiar fluence-distance relation. I discuss the different emission channels that can be expected from the explosion (sub-millimetre, radio, TeV) and their detection challenges. In particular, one of these channels produces an observed wavelength that scales with the redshift following a unique flattened wavelength-distance function, leaving a signature also in the resulting diffuse emission. I conclude presenting the first insights on the cosmological constraints, concerning both the explosive phase and the subsequent remnant phase.

https://arxiv.org/abs/1811.11744
Holographic description of boundary gravitons in (3+1) dimensions
Seth K. Asante, Bianca Dittrich, Hal M. Haggard
(Submitted on 27 Nov 2018)
Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's holographic formulation. Holography holds promise for simplifying computations in quantum gravity. While holographic descriptions of three-dimensional spacetimes and of spacetimes with a negative cosmological constant are well-developed, a complete boundary description of zero curvature, four-dimensional spacetime is not currently available. Building on previous work in three-dimensions, we provide a new route to four-dimensional holography and its boundary gravitons. Using Regge calculus linearized around a flat Euclidean background with the topology of a solid hyper-torus, we obtain the effective action for a dual boundary theory which describes the dynamics of the boundary gravitons. Remarkably, in the continuum limit and at large radii this boundary theory is local and closely analogous to the corresponding result in three-dimensions. The boundary effective action has a degenerate kinetic term that leads to singularities in the one-loop partition function that are independent of the discretization. These results establish a rich boundary dynamics for four-dimensional flat holography.

https://arxiv.org/abs/1812.01542
On the possibility of experimental detection of the discreteness of time
Marios Christodoulou, Carlo Rovelli
(Submitted on 4 Dec 2018 (v1), last revised 8 Dec 2018 (this version, v2))
The Bose-Marletto-Vedral experiment tests a non-relativistic quantum effect due to a gravitational interaction. It has received attention because it may soon be within observational reach in the lab. We observe here that: (i) in relativistic language the experiment tests an interference effect between proper-time intervals; (ii) the relevant difference of proper times is of the order of the Planck time if the masses of the particles in the experiment are of the order of the Planck mass (micrograms); (iii) the experiment might open a window on the structure of time at the Planck scale: if time differences are discrete at this scale ---as quantum gravity research may suggest--- the Planckian discreteness of time could show up as quantum levels of a measurable entanglement entropy.

https://arxiv.org/abs/1812.05127
Quantum gravity and black hole spin in gravitational wave observations: a test of the Bekenstein-Hawking entropy
Eugenio Bianchi, Anuradha Gupta, Hal M. Haggard, B. S. Sathyaprakash
(Submitted on 12 Dec 2018)
Black hole entropy is a robust prediction of quantum gravity with no observational test to date. We use the Bekenstein-Hawking entropy formula to determine the probability distribution of the spin of black holes at equilibrium in the microcanonical ensemble. We argue that this ensemble is relevant for black holes formed in the early universe and predicts the existence of a population of black holes with zero spin. Observations of such a population at LIGO, Virgo, and future gravitational wave observatories would provide the first experimental test of the statistical nature of black hole entropy.

https://arxiv.org/abs/1812.06193
Tullio Regge's legacy: Regge calculus and discrete gravity
John W. Barrett, Daniele Oriti, Ruth M. Williams
(Submitted on 14 Dec 2018)
The review paper "Discrete Structures in Physics", written in 2000, describes how Regge's discretization of Einstein's theory has been applied in classical relativity and quantum gravity. Here, developments since 2000 are reviewed briefly, with particular emphasis on progress in quantum gravity through spin foam models and group field theories.

 

[*now*]

arXiv:1901.04732 [pdf]
Black Hole Evolution Traced Out with Loop Quantum Gravity
Carlo Rovelli
Loop Quantum gravity predicts that black holes evolve into white holes.
Submitted 15 January, 2019; originally announced January 2019.
Appeared as "Viewpoint" in the APS Physics Journal. Slightly edited, completed references
Journal ref: Physics, 11 (2018) 127

arXiv:1901.06454 [pdf, other]
Entropy of a subalgebra of observables and the geometric entanglement entropy
Eugenio Bianchi, Alejandro Satz
The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the vacuum restricted to a region: we consider a subalgebra of observables that has support in the region and a finite resolution. We then define the entropy of a s…
Submitted 18 January, 2019; originally announced January 2019.
21 pagesarXiv:1811.04360 [pdf, ps, other]
2+1D Loop Quantum Gravity on the Edge
Laurent Freidel, Florian Girelli, Barak Shoshany
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space structure into elementary cells, we obtain the loop gravity phase space coupled to a collection of effective particles carrying mass and spin, which measure the curva…
Submitted 8 February, 2019; v1 submitted 11 November, 2018; originally announced November 2018.
44 pages

arXiv:1812.08757 [pdf, other] 10.1103/PhysRevB.99.075123
Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
Lucas Hackl, Lev Vidmar, Marcos Rigol, Eugenio Bianchi
We recently showed [Phys. Rev. Lett. 121, 220602 (2018)] that the average bipartite entanglement entropy of all energy eigenstates of the quantum Ising chain exhibits a universal (for translationally invariant quadratic fermionic models) leading term that scales linearly with the subsystem's volume, while in the thermodynamic limit the first subleading correction does not vanish at the critical fi…
Submitted 12 February, 2019; v1 submitted 20 December, 2018; originally announced December 2018.
11 pages

arXiv:1903.07344 [pdf, other]
Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
Goffredo Chirco, Alex Goeßmann, Daniele Oriti, Mingyi Zhang
We introduce group field theory networks as a generalization of spin networks and of (symmetric) random tensor networks and provide a statistical computation of the Rényi entropy for a bipartite network state using the partition function of a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is sh…
Submitted 18 March, 2019; originally announced March 2019.
40 pages

arXiv:1903.12624 [pdf, other]
Numerical study of the Lorentzian EPRL spin foam amplitude
Pietro Dona, Marco Fanizza, Giorgio Sarno, Simone Speziale
The Lorentzian EPRL spin foam amplitude for loop quantum gravity is a multi-dimensional non-compact integral of highly oscillating functions. Using a method based on the decomposition of Clebsch-Gordan coefficients for the unitary infinite-dimensional representations of SL(2,C) in terms of those of SU(2), we are able to provide for the first time numerical evaluations of the vertex amplitude. The values obtained support the asymptotic formula obtained by Barrett and collaborators with a saddle point approximation, showing, in particular, a power-law decay and oscillations related to the Regge action. The comparison offers a test of the efficiency of the method. Truncating the decomposition to the first few terms provides a qualitative matching of the power-law decay and oscillations. For vector and Euclidean Regge boundary data, a qualitative matching is obtained with just the first term, which corresponds to the simplified EPRL model. We comment on future developments for the numerics and extension to higher vertices. We complete our work with some analytic results: We provide an algorithm and explicit configurations for the different geometries that can arise as boundary data, and explain the geometric consequences of the decomposition used.
Submitted 29 March, 2019; originally announced March 2019.
31 pages

arXiv:1811.02792 [pdf, ps, other]
Coarse graining as a representation change
Norbert Bodendorfer, Fabian Haneder
We discuss how SU(1,1) coherent states from the discrete series allow for a natural coarse graining operation. The physical application are quantum theories based on a set of three extensive observables whose Poisson algebra is isomorphic to su(1,1). In particular, we show that a Perelomov coherent state with representation label Nj0 and spinor label z encodes the physics of N independ…
Submitted 4 April, 2019; v1 submitted 7 November, 2018; originally announced November 2018.
10 pages

arXiv:1904.06149 [pdf, other]
Protected SL(2,R) Symmetry in Quantum Cosmology
Jibril Ben Achour, Etera R. Livine
The polymer quantization of cosmological backgrounds provides an alternative path to the original Wheeler-de Witt (WdW) quantum cosmology, based on a different representation of the canonical variables. The quantum theory of the universe is radically different and leads to quantum superpositions of expanding and contracting quantum geometries, resulting in a quantum bounce. The WdW picture is reco…
Submitted 12 April, 2019; originally announced April 2019.
42 pages

arXiv:1810.09364 [pdf, other]
Bubble Networks: Framed Discrete Geometry for Quantum Gravity
Laurent Freidel, Etera R. Livine
In the context of canonical quantum gravity in 3+1 dimensions, we introduce a new notion of bubble network that represents discrete 3d space geometries. These are natural extensions of twisted geometries, which represent the geometrical data underlying loop quantum geometry and are defined as networks of SU(2) holonomies. In addition to the SU(2) representations encoding the geometrical flux, the…
Submitted 13 February, 2019; v1 submitted 22 October, 2018; originally announced October 2018.
15 pages

arXiv:1904.07046 [gr-qc](or arXiv:1904.07046v1 [gr-qc] for this version)
Bouncing evolution in a model of loop quantum gravity
Cong Zhang, Jerzy Lewandowski, Haida Li, Yongge Ma
(Submitted on 15 Apr 2019)
To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The Hamiltonian operator H^v is chosen to be graph-preserving, and the matrix elements of H^v are explicitly worked out in a suitable basis. The non-trivial Euclidean part H^Ev of H^v is studied in details. It turns out that by choosing a specific symmetrization of H^Ev, the dynamics driven by the Hamiltonian gives a picture of bouncing evolution. Our result in the model of full loop quantum gravity gives a significant echo of the well-known quantum bounce in the symmetry-reduced model of loop quantum cosmology, which indicates a closed relation between singularity resolution and quantum geometry.
27 pages

arXiv:1812.10996 [pdf, other]
Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
Eugenio Bianchi, Pietro Dona, Ilya Vilensky
Bell-network states are loop-quantum-gravity states that glue quantum polyhedra with entanglement. We present an algorithm and a code that evaluates the reduced density matrix of a Bell-network state and computes its entanglement entropy. In particular, we use our code for simple graphs to study properties of Bell-network states and to show that they are non-typical in the Hilbert space. Moreover,…
Submitted 17 April, 2019; v1 submitted 28 December, 2018; originally announced December 2018.
26 pages

arXiv:1901.09173 [gr-qc](or arXiv:1901.09173v2 [gr-qc] for this version)
Cyclic Szekeres Universes
John D. Barrow, Andronikos Paliathanasis
(Submitted on 26 Jan 2019 (v1), last revised 18 Apr 2019 (this version, v2))
We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state pg=(γ−1)ρg, where γ is a constant. The field equations determine two families of spacetimes which describe homogeneous Kantowski-Sachs universes and inhomogeneous Friedmann universe. The ghost field Einstein permits static and cyclic solutions to exist. The stability of the Einstein static and cyclic solutions are studied with a critical point analysis.
10 pagesarXiv:1904.11338 [pdf, other]
A minisuperspace model of compact phase space gravity
Danilo Artigas Guimarey, Jakub Mielczarek, Carlo Rovelli
The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The purpose of this article is to study the idea of generalizing the theory of gravity by compactification of the phase space. We investigate the procedure of compactification of the phase space on a minisuperspace gravitational model with two dimensional phase space. In the affine limit, the model reduces to the flat de Sitter cosmology. The phase space is generalized to the spherical case, and the case of loop quantum cosmology is recovered in the cylindrical phase space limit. Analysis of the dynamics reveals that the compactness of the phase space leads to both UV and IR effects. In particular, the phase of re-collapse appears, preventing the universe from expanding to infinite volume. Furthermore, the quantum version of the model is investigated and the quantum constraint is solved. As an example, we analyze the case with the spin quantum number s=2, for which we determine transition amplitude between initial and final state of the classical trajectory. The probability of the transition is peaked at Λ=0.
Submitted 25 April, 2019; originally announced April 2019.
13 pages

arXiv:1904.11906 [pdf, ps, other]
Bi-gravity with a single graviton
Sergei Alexandrov, Simone Speziale
We analyze a bi-gravity model based on the first order formalism, having as fundamental variables two tetrads but only one Lorentz connection. We show that on a large class of backgrounds its linearization agrees with general relativity. At the non-linear level, additional degrees of freedom appear, and we reveal the mechanism hiding them around the special backgrounds. We further argue that they do not contain a massive graviton, nor the Boulware-Deser ghost. The model thus propagates only one graviton, whereas the nature of the additional degrees of freedom remains to be investigated. We also present a foliation-preserving deformation of the model, which keeps all symmetries except time diffeomorphisms and has three degrees of freedom.
Submitted 26 April, 2019; originally announced April 2019.
29 pages

arXiv:1904.13269 [gr-qc](or arXiv:1904.13269v1 [gr-qc] for this version)
Renormalisation with SU(1, 1) coherent states on the LQC Hilbert space
Norbert Bodendorfer, Dennis Wuhrer
(Submitted on 30 Apr 2019)
We describe how SU(1,1) Perelomov coherent states can be constructed and used on the standard LQC Hilbert space. At a technical level, this requires us to find a factor ordering for the operators representing the so called CVH algebra that preserves its classical SU(1,1) structure. We present such a (rather involved) ordering choice. This allows us to transfer recently established results on coarse graining cosmological states from direct quantisations of the CVH algebra to the standard loop quantum cosmology (LQC) Hilbert space and full theory embeddings thereof. We explicitly discuss how the SU(1,1) representation spaces used in this latter approach are embedded into the LQC Hilbert space and how the SU(1,1) representation label sets a lower cut-off for the loop quantum gravity spins (= U(1) representation labels in LQC). Our results provide an explicit example of a non-trivial renormalisation group flow with a scale set by the SU(1, 1) representation label and interpreted as the minimally resolved geometric scale.
15 pages

arXiv:1905.00348 [pdf, other]
Self-duality of the 6j-symbol and Fisher zeros for the Tetrahedron
Valentin Bonzom, Etera R. Livine
The relation between the 2d Ising partition function and spin network evaluations, reflecting a bulk-boundary duality between the 2d Ising model and 3d quantum gravity, promises an exchange of results and methods between statistical physics and quantum geometry. We apply this relation to the case of the tetrahedral graph. First, we find that the high/low temperature duality of the 2d Ising model translates into a new self-duality formula for Wigner's 6j-symbol from the theory of spin recoupling. Second, we focus on the duality between the large spin asymptotics of the 6j-symbol and Fisher zeros. Using the Ponzano-Regge formula for the asymptotics for the 6j-symbol at large spins in terms of the tetrahedron geometry, we obtain a geometric formula for the zeros of the (inhomogeneous) Ising partition function in terms of triangle angles and dihedral angles in the tetrahedron. While it is well-known that the 2d intrinsic geometry can be used to parametrize the critical point of the Ising model, e.g. on isoradial graphs, it is the first time to our knowledge that the extrinsic geometry is found to also be relevant.This outlines a method towards a more general geometric parametrization of the Fisher zeros for the 2d Ising model on arbitrary graphs.
Submitted 1 May, 2019; originally announced May 2019.
29 pages

 

[*now*]

arXiv:1901.01279 [pdf, other]
Von Neumann stability of modified loop quantum cosmologies
Sahil Saini, Parampreet Singh
Von Neumann stability analysis of quantum difference equations in loop quantized spacetimes has often proved useful to understand viability of quantizations and whether general relativistic description is recovered at small spacetime curvatures. We use this technique to analyze the infrared behavior of quantum Hamiltonian constraint in recently explored modifications of loop quantum cosmology: mLQC-I and mLQC-II, for the spatially flat FLRW model. We investigate the behavior for μo scheme, where minimum area of loops in quantization procedure does not take physical metric into account, and the μ¯ scheme where quantization procedure uses physical metric. The fate of stability of quantum difference equations is tested for massless scalar field as well as with inclusion of a positive cosmological constant. We show that for mLQC-I and mLQC-II, difference equation fails to be von Neumann stable for the μo scheme if cosmological constant is included signaling problematic behavior at large volumes. Both of the modified loop quantum cosmologies are von Neumann stable for μ¯ scheme. In contrast to standard loop quantum cosmology, properties of roots turn out to be richer and intricate. Our results demonstrate the robustness of μ¯ scheme (or `improved dynamics') in loop quantization of cosmological spacetimes even when non-trivial quantization ambiguities of Hamiltonian are considered, and show that μo scheme is non-viable in this setting.
25 pages

arXiv:1901.08161 [pdf, other]
An octahedron of complex null rays, and conformal symmetry breaking
Maciej Dunajski, Miklos Långvik, Simone Speziale
We show how the manifold T∗SU(2,2) arises as a symplectic reduction from eight copies of the twistor space. Some of the constraints in the twistor space correspond to an octahedral configuration of twelve complex light rays in the Minkowski space. We discuss a mechanism to break the conformal symmetry down to the twistorial parametrisation of T∗SL(2,C) used in loop quantum gravity.
Submitted 16 May, 2019; v1 submitted 23 January, 2019; originally announced January 2019.
10 pages

arXiv:1905.07251 [pdf, other]
Evaporating black-to-white hole
Pierre Martin-Dussaud, Carlo Rovelli
We construct and discuss the form of the (effective) spacetime geometry inside a black hole undergoing a quantum transition to a white hole, taking into account the back-reaction of the component of the Hawking radiation falling into the hole.
Submitted 17 May, 2019; originally announced May 2019.

arXiv:1905.10382 [gr-qc](or arXiv:1905.10382v1 [gr-qc] for this version)
The cosmology of minimal varying Lambda theories
Stephon Alexander, Marina Cortês, Andrew R. Liddle, João Magueijo, Robert Sims, Lee Smolin
(Submitted on 24 May 2019)
Inserting a varying Lambda in Einstein's field equations can be made consistent with Bianchi identities by allowing for torsion, without the need for adding scalar field degrees of freedom. In the minimal such theory, in the absence of matter Lambda is totally free and undetermined by the field equations. Inclusion of matter ties Lambda algebraically to it, at least in a set up where homogeneity and isotropy are assumed, i.e.\ when there is no Weyl curvature. We show that Lambda is proportional to the matter density, with a proportionality constant that depends on the equation of state. Unfortunately, the proportionality constant becomes infinite for pure radiation, ruling out the minimal theory {\it prima facie}, in spite of its novel internal consistency. It is possible to generalize the theory still without the addition of kinetic terms (which would bring it close to a more conventional quintessence model). We now find a new algebraically-enforced proportionality between Lambda and the matter density. Lambda and radiation may now coexist in a form consistent with Big Bang nucleosynthesis, though this places strict constraints on the single free parameter of the theory, θ. In the matter epoch Lambda behaves just like a dark matter component. Its density is proportional to the baryonic and/or dark matter, and its presence and gravitational effects would need to be included in accounting for the necessary dark matter in our Universe. This is a companion paper to Ref. [1] where the underlying gravitational theory is developed in detail.
Companion paper submitted simultaneously to gr-qc

arXiv:1812.05403 [pdf, ps, other]
Classical axisymmetric gravity in real Ashtekar variables
Rodolfo Gambini, Esteban Mato, Javier Olmedo, Jorge Pullin
(Submitted on 13 Dec 2018 (v1), last revised 30 May 2019 (this version, v2))
We formulate axisymmetric general relativity in terms of real Ashtekar--Barbero variables. We study the constraints and equations of motion and show how the Kerr, Schwarzschild and Minkowski solutions arise. We also discuss boundary conditions. This opens the possibility of a midisuperspace quantization using loop quantum gravity techniques for spacetimes with axial symmetry and time dependence.
14 pages

arXiv:1904.08370 [pdf, other]
Typical entropy of a subsystem: Page curve and its variance
Eugenio Bianchi, Pietro Dona
In a quantum system in a pure state, a subsystem generally has a non-zero entropy because of entanglement with the rest of the system. Is the average entanglement entropy of pure states also the typical entropy of the subsystem? The exact formula for the average ⟨SA⟩ was conjectured by Page in 1995 and later proved. Here we compute the exact formula for the average entropy and v…
Submitted 1 June, 2019; v1 submitted 17 April, 2019; originally announced April 2019.
5 pages

arXiv:1902.03590 [pdf, other]
Spectral estimators for finite non-commutative geometries
John W. Barrett, Paul Druce, Lisa Glaser
(Submitted on 10 Feb 2019 (v1), last revised 3 Jun 2019 (this version, v3))
A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addreses the question of how to extract information about these geometries from the spectrum of the Dirac operator. Since the Dirac operator is a finite-dimensional matrix, the usual asymptotics of the eigenvalues makes no sense and is replaced by measurements of the spectrum at a finite energy scale. The spectral dimension of the square of the Dirac operator is improved to provide a new spectral measure of the dimension of a space called the spectral variance. Similarly, the volume of a space can be computed from the spectrum once the dimension is known. Two methods of doing this are investigated: the well-known Dixmier trace and a recent improvement due to Abel Stern. Finally, the distance between two geometries is investigated by comparing the spectral zeta functions using the method of Cornelissen and Kontogeorgis. All of these techniques are tested on the explicit examples of the fuzzy spheres and fuzzy tori, which can be regarded as approximations of the usual Riemannian sphere and flat tori. Then they are applied to characterise some random fuzzy spaces using data generated by a Monte Carlo simulation.
27 pages

arXiv:1906.01628 [pdf, other]
Spectroscopy of spinons in Coulomb quantum spin liquids
Siddhardh C. Morampudi, Frank Wilczek, Chris R. Laumann
(Submitted on 4 Jun 2019)
We calculate the effect of the emergent photon on threshold production of spinons in U(1) Coulomb spin liquids such as quantum spin ice. The emergent Coulomb interaction modifies the threshold production cross-section dramatically, changing the weak turn-on expected from the density of states to an abrupt onset reflecting the basic coupling parameters. The slow photon typical in existing lattice models and materials suppresses the intensity at finite momentum and allows profuse Cerenkov radiation beyond a critical momentum. These features are broadly consistent with recent numerical and experimental results.
5 pages

arXiv:1906.02211 [pdf, other]
Primordial fluctuations from quantum gravity
Francesco Gozzini, Francesca Vidotto
We study fluctuations and correlations between spatial regions, generated by the primordial quantum gravitational phase of the universe. We do so by a numerical evaluation of Lorentzian amplitudes in Loop Quantum Gravity, in a non-semiclassical regime. We find that the expectation value of the quantum state of the geometry emerging from the early quantum phase of the universe is a homogeneous spac…
Submitted 5 June, 2019; originally announced June 2019.
8 pages

arXiv:1906.04792 [pdf, ps, other]
Quantization of dynamical symplectic reduction
Martin Bojowald, Artur Tsobanjan
A long-standing problem in quantum gravity and cosmology is the quantization of systems in which evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented, together with new structures and results that prove the existence of specific conditions for well-defined evolution to be possible.
Submitted 11 June, 2019; originally announced June 2019.
37 pages

arXiv:1906.02958 [gr-qc](or arXiv:1906.02958v1 [gr-qc] for this version)
Black hole quantum atmosphere for freely falling observers
Ramit Dey, Stefano Liberati, Zahra Mirzaiyan, Daniele Pranzetti
(Submitted on 7 Jun 2019)
We analyze Hawking radiation as perceived by a freely-falling observer and try to draw an inference about the region of origin of the Hawking quanta. To do so, first we calculate the energy density from the stress energy tensor, as perceived by a freely-falling observer. Then we compare this with the energy density computed from an effective temperature functional which depends on the state of the observer. The two ways of computing these quantities show a mismatch at the light ring outside the black hole horizon. To better understand this ambiguity, we show that even taking into account the (minor) breakdown of the adiabatic evolution of the temperature functional which has a peak in the same region of the mismatch, is not enough to remove it. We argue that the appearance of this discrepancy can be traced back to the process of particle creation by showing how the Wentzel--Kramers--Brillouin approximation for the field modes breaks down between the light ring at 3M and 4M, with a peak at r=3.3M exactly where the energy density mismatch is maximized. We hence conclude that these facts strongly support a scenario where the Hawking flux does originate from a "quantum atmosphere" located well outside the black hole horizon.

arXiv:1906.07113 [pdf, ps, other]
Generalized Gibbs Ensembles in Discrete Quantum Gravity
Goffredo Chirco, Isha Kotecha
Maximum entropy principle and Souriau's symplectic generalization of Gibbs states have provided crucial insights leading to extensions of standard equilibrium statistical mechanics and thermodynamics. In this brief contribution, we show how such extensions are instrumental in the setting of discrete quantum gravity, towards providing a covariant statistical framework for the emergence of continuum…
Submitted 17 June, 2019; originally announced June 2019.
8 pages

arXiv:1906.03872 [pdf, ps, other]
Dynamics of Einstein-Aether Scalar field Cosmology
Andronikos Paliathanasis, G. Papagiannopoulos, Spyros Basilakos, John D. Barrow
(Submitted on 10 Jun 2019)
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two separate where a pressureless fluid source is included or absent. In particular, we determine the critical points of the field equations and we study the stability of the specific solutions. The limit of general relativity is fully recovered, while the dynamical system admits de Sitter solutions which can describe the past inflationary era and the future late-time attractor. Results for generic scalar field potentials are presented while some numerical behaviours are given for specific potential forms.

arXiv:1906.07876 [pdf, other]
Gravitational edge modes: From Kac-Moody charges to Poincaré networks
Laurent Freidel, Etera R. Livine, Daniele Pranzetti
We revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges. Partitioning the space manifold into 3D regions glued together th…
Submitted 18 June, 2019; originally announced June 2019.
43 pages

arXiv:1906.05633 [pdf, ps, other]
Isospectrality of quasinormal modes for black holes beyond Schwarzschild
Flora Moulin, Aurélien Barrau
The reason why the equations describing axial and polar perturbations of the Schwarzschild black hole have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on uncharged and non-rotating black holes, we extend the results to slightly more general metrics.
Submitted 13 June, 2019; originally announced June 2019.

arXiv:1906.00603 [pdf, other]
Quasinormal modes of black holes in a toy-model for cumulative quantum gravity
Aurélien Barrau, Killian Martineau, Jeremy Martinon, Flora Moulin
The idea that quantum gravity effects might leak outside the horizon of a black hole has recently been intensively considered. In this study, we calculate the quasinormal modes as a function of the location and amplitude of a generic metric perturbation distorting to the Schwarzschild spacetime. We conclude on the possible observability of quantum metric corrections by current and future gravitati…
Submitted 18 June, 2019; v1 submitted 3 June, 2019; originally announced June 2019.

arXiv:1812.03550 [pdf, other]
Spin foam models and the Duflo map
Marco Finocchiaro, Daniele Oriti
We give a general definition of spin foam models, and then of models of 4d quantum gravity based on constraining BF theory. We highlight the construction and quantization ambiguities entering model building, among which the choice of quantization map applied to the B variables carrying metric information after imposing simplicity constraints, and the different strategies for imposing the latter co…
Submitted 18 June, 2019; v1 submitted 9 December, 2018; originally announced December 2018.
20 pages

 

[suprised]

Here some update from an expert: https://arxiv.org/pdf/2002.05703.pdf

From the conclusions: "At present, it is not possible to derive a sufficiently complete effective theory from full loop quantum gravity, and even if this were possible, it is not clear whether loop quantum gravity itself is covariant and consistent."

This was long overdue!