Loop-and-allied QG bibliography

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Repulsive gravity induced by a conformally coupled scalar field implies a bouncing radiation-dominated universe
Vicente Antunes, Mario Novello
(Submitted on 8 Mar 2017)
In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity [1]. When the scalar field vacuum is in a broken symmetry state, an effective gravitational constant emerges which, in certain regimes, can lead to gravitational repulsive effects when only ordinary radiation is coupled to gravity. In this case, a bouncing universe is shown to be the only cosmological solution admissible by the field equations when the scalar field is in such a broken symmetry state.
Comments: 10 pages, 1 figure
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1703.03060 [gr-qc]

Poincaré gauge gravity: an emergent scenario
J.L. Chkareuli
(Submitted on 4 Mar 2017)
The Poincar\'e gauge gravity (PGG) with the underlying vector fields of tetrads and spin-connections is perhaps the best theory candidate for gravitation to be unified with the other three elementary forces of nature. There is a clear analogy between local frame in PGG and local internal symmetry space in the Standard Model. As a result, the spin-connection fields, gauging the local frame Lorentz symmetry group SO(1,3)_{LF}, appear in PGG much as photons and gluons appear in SM. We propose that such an analogy may follow from their common emergent nature allowing to derive PGG in the same way as conventional gauge theories. In essence, we start with an arbitrary theory of some vector and fermion fields which possesses only global spacetime symmetries, such as Lorentz and translational invariance, in flat Minkowski space. The two vector field multiplets involved are proposed to belong, respectively, to the adjoint (A_{{\mu}}^{ij}) and vector (e_{{\mu}}^{i}) representations of the starting global Lorentz symmetry. We show that if these prototype vector fields are covariantly constrained, A_{{\mu}}^{ij}A_{ij}^{{\mu}}=M_{A} and e_{{\mu}}^{i}e_{i}^{{\mu}}=M_{e}, thus causing a spontaneous violation of the accompanying global symmetries (M_{A,e} are their proposed violation scales), then the only possible theory compatible with these length-preserving constraints is turned out to be the gauge invariant PGG, while the corresponding massless (pseudo)Goldstone modes are naturally collected in the emergent gauge fields of tetrads and spin-connections. In a minimal theory case being linear in a curvature we unavoidably come to the Einstein-Cartan theory. The extending theories with propagating spin-connection and tetrad modes are also considered and their possible unification with the Standard Model is briefly discussed.
Comments: 33 pages, submitted to Physical Review D. arXiv admin note: text overlap with arXiv:1305.6898
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1703.01492 [gr-qc]
Gravastars in f(R,T) gravity
Amit Das, Shounak Ghosh, Swapan Das, B.K. Guha, Saibal Ray
(Submitted on 26 Feb 2017)
We propose a unique stellar model under the f(R,T) gravity by using the conjecture of Mazur-Mottola~\cite{Mazur2001,Mazur2004} which is known as gravastar and a viable alternative to the black hole as available in literature. This gravastar is described by the three different regions, viz., (I) Interior core region, (II) Intermediate thin shell, and (III) Exterior spherical region. The pressure within the interior region is equal to the constant negative matter density which provides a repulsive force over the thin spherical shell. This thin shell is assumed to be formed by a fluid of ultra relativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zel'dovich's conjecture of stiff fluid~\cite{zeldovich1972}, does counter balance the repulsive force exerted by the interior core region. The exterior spherical region is completely vacuum and assumed to be de Sitter spacetime which can be described by the Schwarzschild solution. Under this specification we find out a set of exact and singularity-free solution of the collapsing star which presents several other physically valid features within the framework of alternative gravity.
Comments: 7 pages, 4 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1702.08873 [gr-qc]
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Poincaré Gauge Gravity Cosmology
Hongchao Zhang, Lixin Xu
(Submitted on 2 Mar 2017)
In this work, we construct the logical framework of the Poincar\'e gauge gravity cosmology based on five postulations, and introduce the modified redshift relation within this framework. Then we solve a system with quadratic action and some other assumptions to get an analytic solution on background level. The evolution of the Universe on background can be reproduced from this solution without hypothesizing dark energy. Further, we use the type Ia supernova data set JLA to test the effect of the modified redshift relation under the constraints of system parameters. The results show that the constraint on some parameters are compact.
Comments: 5 pages, 3 figures, 2 tables
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1703.00639 [gr-qc]
(or arXiv:1703.00639v1 [gr-qc] for this version)
Analogue Gravity Models From Conformal Rescaling
Sabine Hossenfelder, Tobias Zingg
(Submitted on 13 Mar 2017)
Analogue gravity is based on a mathematical identity between quantum field theory in curved space-time and the propagation of perturbations in certain condensed matter systems. But not every curved space-time can be simulated in such a way, because one does not only need a condensed matter system that generates the desired metric tensor, but that system then also has to obey its own equations of motion. And specifying the metric tensor that one wishes to realize usually overdetermines the underlying condensed matter system, such that its equations of motion are in general not fulfilled, in which case the desired metric does not have an analogue.
Here, we show that the class of metrics that have an analogue is bigger than what a first cursory consideration might suggest. This is due to the analogue metric only being defined up to a choice of parametrization of the perturbation in the underlying condensed matter system. In this way, the class of analogue gravity models can be vastly expanded. In particular, we demonstrate how this freedom of choice can be used to insert an intermediary conformal factor. Then, as a corollary, we find that any metric conformal to a Painlev\'e--Gullstrand type line element can, potentially, result as an analogue of a perturbation propagating in a non-viscous, barotropic fluid.
Comments: 12 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
MSC classes: 83-XX
Cite as: arXiv:1703.04462 [gr-qc]
(or arXiv:1703.04462v1 [gr-qc] for this version)
Gravitational echoes from macroscopic quantum gravity effects
Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay
(Submitted on 31 Jan 2017 (v1), last revised 1 Feb 2017 (this version, v2))
New theoretical approaches developed in the last years predict that macroscopic quantum gravity effects in black holes should lead to modifications of the gravitational wave signals expected in the framework of classical general relativity, with these modifications being characterized by the existence of dampened repetitions of the primary signal. Here we use the fact that non-perturbative corrections to the near-horizon external geometry of black holes are necessary for these modifications to exist, in order to classify different proposals and paradigms with respect to this criterion and study in a neat and systematic way their phenomenology. Proposals that lead naturally to the existence of echoes in the late-time ringdown of gravitational wave signals from black hole mergers must share the replacement of black holes by horizonless configurations with a physical surface showing reflective properties in the relevant range of frequencies. On the other hand, proposals or paradigms that restrict quantum gravity effects on the external geometry to be perturbative, such as black hole complementarity or the closely related firewall proposal, do not display echoes. For the sake of completeness we exploit the interplay between the timescales associated with the formation of firewalls and the mechanism behind the existence of echoes in order to conclude that even unconventional distortions of the firewall concept (such as naked firewalls) do not lead to this phenomenon.
Comments: V1: 21 pages + references, 1 figure. V2: updated references
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Astrophysical Phenomena (astro-ph.HE); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1701.09156 [gr-qc]
Flowing to the continuum in discrete tensor models for quantum gravity
Astrid Eichhorn, Tim Koslowski
(Submitted on 11 Jan 2017)
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group fixed point in a setup where the tensor size N serves as the Renormalization Group scale. We develop functional Renormalization Group tools for tensor models with a main focus on a rank-3 model for three-dimensional quantum gravity. We rediscover the double-scaling limit and provide an estimate for the scaling exponent. Moreover, we identify two additional fixed points with a second relevant direction in a truncation of the Renormalization Group flow. The new relevant direction might hint at the presence of additional degrees of freedom in the corresponding continuum limit.
Comments: 16 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1701.03029 [gr-qc]
(or arXiv:1701.03029v1 [gr-qc] for this version)
Quantum Metric and Entanglement on Spin Networks
Fabio M. Mele
(Submitted on 19 Mar 2017)
Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the formalism of Geometric Quantum Mechanics (GQM) to give a tensorial characterization of entanglement on spin network states. Our analysis focuses on the simple case of a single link graph (Wilson line state) for which we define a dictionary to construct a Riemannian metric tensor and a symplectic structure on the space of states. The manifold of (pure) quantum states is then stratified in terms of orbits of equally entangled states and the block-coefficient matrices of the corresponding pulled-back tensors fully encode the information about separability and entanglement. In particular, the off-diagonal blocks define an entanglement monotone interpreted as a distance with respect to the separable state. As such, it provides a measure of graph connectivity. Finally, in the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link. This suggests a connection between the GQM formalism and the (simplicial) geometric properties of spin network states through entanglement.
Comments: 162 pages, 11 figures, Master Thesis
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
Cite as: arXiv:1703.06415 [gr-qc]

Fisher Metric, Geometric Entanglement and Spin Networks
Goffredo Chirco, Fabio M. Mele, Daniele Oriti, Patrizia Vitale
(Submitted on 15 Mar 2017)
We introduce the geometric formulation of Quantum Mechanics in the quantum gravity context, and we use it to give a tensorial characterization of entanglement on spin network states. Starting from the simplest case of a single-link graph (Wilson line), we define a dictionary to construct a Riemannian metric tensor and a symplectic structure on the space of spin network states, showing how they fully encode the information about separability and entanglement, and, in particular, an entanglement monotone interpreted as a distance with respect to the separable state. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We extend then such analysis to the study of non-local correlations between two non-adjacent regions of a generic spin network. In the end, our analysis shows that the same spin network graph can be understood as an information graph whose connectivity encodes, both at the local and non-local level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.
Comments: 51 pages, 3 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
Cite as: arXiv:1703.05231 [gr-qc]

Holographic spin networks from tensor network states
Sukhwinder Singh, Nathan A. McMahon, Gavin K. Brennen
(Submitted on 1 Feb 2017)
In the holographic correspondence of quantum gravity, a global onsite symmetry at the boundary generally translates to a local gauge symmetry in the bulk. In this paper, we extend the tensor network based toy model for holography introduced in [arXiv:1701.04778] to incorporate this feature. We lift the multi-scale renormalization ansatz (MERA) representation of the ground state of a one dimensional (1D) local Hamiltonian, which has a global onsite symmetry, to a dual quantum state of a 2D lattice on which the symmetry appears gauged. We show how the 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining bulk degrees of freedom that are not fixed by the symmetry. (In analogy with the holographic correspondence, we interpret the latter to possibly include "gravitational" degrees of freedom.) We illustrate these features for a particular subset of bulk states referred to as copy bulk states. We present numerical results for ground states of several 1D critical spin chains to illustrate that: (i) entanglement in the dual copy bulk states potentially depends on the central charge of the underlying conformal field theories, and (ii) the spectrum of a bulk density matrix, obtained by tracing out the gauge degrees of freedom, exhibits degeneracies, possibly suggesting an emergent symmetry in the non-gauge sector of the bulk. We also illustrate the possibility of emergent topological order in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.
Comments: 21 pages, 18 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
Cite as: arXiv:1702.00392 [cond-mat.str-el]
On the fate of the Hoop Conjecture in quantum gravity
Fabio Anzà, Goffredo Chirco
(Submitted on 15 Mar 2017 (v1), last revised 21 Mar 2017 (this version, v2))
We consider a closed region R of 3d quantum space modeled by SU(2) spin-networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interprete such phenomenon as a pre-geometric analogue of Thorne's "Hoop conjecture", at the core of the formation of a horizon in General Relativity.
Comments: 7 pages, 2 figures, minor improvements
Subjects: General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
Cite as: arXiv:1703.05241 [gr-qc]
Naturalizing Gravity of the Quantum Fields, and the Hierarchy Problem
Durmus Demir
(Submitted on 10 Mar 2017)
It is shown that gravity can be incorporated into the Standard Model (SM) in a way solving the hierarchy problem. For this, the SM effective action in flat spacetime is adapted to curved spacetime via not only the general covariance but also the gauge invariance. For the latter, gauge field hard masses, induced by loops at the UV scale Λ, are dispelled by construing Λ as the constant value assigned to curvature. This gives way to an unprecedented mechanism for incorporating gravity into the SM in that the hierarchy problem is solved by transmutation of the Higgs boson Λ2--mass into the Higgs-curvature coupling, and the cosmological constant problem is alleviated by metamorphosis of the vacuum Λ4--energy into the Einstein-Hilbert term. Gravity emerges correctly if the SM is accompanied by a secluded dark sector sourcing non-interacting dark matter, dark energy and dark radiation. Physics beyond the SM, containing Higgs-phobic scalars that resolve the strong CP problem, flavor problem, baryogenesis and inflation, respects the hierarchy. Majorana neutrinos are naturally incorporated if Λ lies at the see-saw scale. This mechanism, in general, leaves no compelling reason to anticipate new particles at the LHC or higher-energy colliders.
Comments: 27 pages, 2 tables
Subjects: High Energy Physics - Phenomenology (hep-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)


Science Advisor
The Overview Chapter in Loop Quantum Gravity: The First 30 Years
Abhay Ashtekar, Jorge Pullin
(Submitted on 21 Mar 2017)
This is the introductory Chapter in the monograph Loop Quantum Gravity: The First 30 Years, edited by the authors, that was just published in the series "100 Years of General Relativity. The 8 invited Chapters that follow provide fresh perspectives on the current status of the field from some of the younger and most active leaders who are currently shaping its development. The purpose of this Chapter is to provide a global overview by bridging the material covered in subsequent Chapters. The goal and scope of the monograph is described in the Preface which can be read by following the Front Matter link at the website listed below.

Evolution of Universes in Causal Set Cosmology
Fay Dowker, Stav Zalel
(Submitted on 22 Mar 2017)
The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential Growth (CSG) models of Rideout and Sorkin form an interesting class of such laws. It has been shown that a renormalisation of the dynamical parameters of a CSG model occurs whenever the universe undergoes a Big Crunch-Big Bang bounce. In this paper we propose a way to model the creation of a new universe after the singularity of a black hole. We show that renormalisation of dynamical parameters occurs in a CSG model after such a creation event. We speculate that this could realise aspects of Smolin's Cosmological Natural Selection proposal.
Fermions in Loop Quantum Cosmology
Beatriz Elizaga Navascués, Mercedes Martín-Benito, Guillermo A. Mena Marugán
(Submitted on 30 Mar 2017)
This work pioneers the quantization of primordial fermion perturbations in hybrid Loop Quantum Cosmology (LQC). We consider a Dirac field coupled to a spatially flat, homogeneous, and isotropic cosmology, sourced by a scalar inflaton, and treat the Dirac field as a perturbation. We describe the inhomogeneities of this field in terms of creation and annihilation variables, chosen to admit a unitary evolution if the Dirac fermion were treated as a test field. Considering instead the full system, we truncate its action at quadratic perturbative order and construct a canonical formulation. In particular this implies that, in the global Hamiltonian constraint of the model, the contribution of the homogeneous sector is corrected with a quadratic perturbative term. We then adopt the hybrid LQC approach to quantize the full model, combining the loop representation of the homogeneous geometry with the Fock quantization of the inhomogeneities. We assume a Born-Oppenheimer ansatz for physical states and show how to obtain a Schr\"odinger equation for the quantum evolution of the perturbations, where the role of time is played by the homogeneous inflaton. We prove that the resulting quantum evolution of the Dirac field is indeed unitary, despite the fact that the underlying homogeneous geometry has been quantized as well. Remarkably, in such evolution, the fermion field couples to an infinite sequence of quantum moments of the homogeneous geometry. Moreover, the evolved Fock vacuum of our fermion perturbations is shown to be an exact solution of the Schr\"odinger equation. Finally, we discuss in detail the quantum backreaction that the fermion field introduces in the global Hamiltonian constraint. For completeness, our quantum study includes since the beginning (gauge-invariant) scalar and tensor perturbations, that were studied in previous works.
Comments: 38 pages. Prepared to submit to JCAP
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1703.10391 [gr-qc]

Loop quantum cosmology and singularities
Ward Struyve
(Submitted on 30 Mar 2017)
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. In order to base this belief on theoretical analysis, the notorious problems such as the problem of time and the problem of the actual meaning of singularities must be addressed and eventually overcome. In this paper, we address the problem of singularities in the context of the Bohmian formulation of loop quantum cosmology (which describes symmetry-reduced models of quantum gravity using the quantization techniques of loop quantum gravity). This formulation solves the mentioned conceptual problems. For example the notion of singularity is clear in this case, since there is an actual metric in addition to the wave function. As such, there is a singularity whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-time with arbitrary constant spatial curvature and possibly a cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This result is obtained without assuming any boundary conditions. This result should also be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist (depending on the wave function and the initial conditions for the metric and scalar field).
Comments: 17 pages, no figures, LaTeX
Subjects: General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
Cite as: arXiv:1703.10274 [gr-qc]
(or arXiv:1703.10274v1 [gr-qc] for this version)

Black Holes in Loop Quantum Gravity
Alejandro Perez
(Submitted on 27 Mar 2017)
This is a review of the results on black hole physics in the framework of loop quantum gravity. The key feature underlying the results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum gravity. Quantum discreteness follows directly from the canonical quantization prescription when applied to the action of general relativity that is suitable for the coupling of gravity with gauge fields and specially with Fermions. Planckian discreteness and causal considerations provide the basic structure for the understanding of the thermal properties of black holes close to equilibrium. Discreteness also provides a fresh new look at more (at the moment) speculative issues such as those concerning the fate of information in black hole evaporation. The hypothesis of discreteness leads also to interesting phenomenology with possible observational consequences. The theory of loop quantum gravity is a developing program. This review reports its achievements and open questions in a pedagogical manner with an emphasis on quantum aspects of black hole physics.
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1703.09149 [gr-qc]
(or arXiv:1703.09149v1 [gr-qc] for this version)

Inflation and Bounce from Classical and Loop Quantum Cosmology Imperfect Fluids
V.K. Oikonomou
(Submitted on 27 Mar 2017)
We investigate how various inflationary and bouncing cosmologies can be realized by imperfect fluids with a generalized equation of state, in the context of both classical and loop quantum cosmology. With regards to the inflationary cosmologies, we study the intermediate inflation scenario, the R2 inflation scenario and two constant-roll inflation scenarios and with regards to the bouncing cosmologies we study the matter bounce scenario, the singular bounce and the super bounce scenario. Within the context of the classical cosmology, we calculate the spectral index of the power spectrum of primordial curvature perturbations, the scalar-to-tensor ratio and the running of the spectral index and we compare the resulting picture with the Planck data. As we demonstrate, partial compatibility with the observational data is achieved in the imperfect fluid description, however none of the above scenarios is in full agreement with data. This result shows that although it is possible to realize various cosmological scenarios using different theoretical frameworks, it is not guaranteed that all the theoretical descriptions are viable.
Comments: IJMPD Accepted
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1703.09009 [gr-qc]
(or arXiv:1703.09009v1 [gr-qc] for this version)
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Resolving Cosmological Singularities
Ali H. Chamseddine, Viatcheslav Mukhanov
(Submitted on 18 Dec 2016)
We find a simple modification of the longitudinal mode in General Relativity which incorporates the idea of limiting curvature. In this case the singularities in contracting Friedmann and Kasner universes are avoided, and instead, the universe has a regular bounce which takes place during the time inversely proportional to the square root of the limiting curvature. Away from the bounce, corrections to General Relativity are negligible. In addition the non-singluar modification of General Relativity delivers for free a realistic candidate for Dark Matter.
Comments: 15 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)
DOI: 10.1088/1475-7516/2017/03/009
Cite as: arXiv:1612.05860 [gr-qc]
(or arXiv:1612.05860v1 [gr-qc] for this version)

General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1703.10670 [gr-qc]
(or arXiv:1703.10670v1 [gr-qc] for this version)
General Relativity and Quantum Cosmology
Effective loop quantum cosmology as a higher-derivative scalar-tensor theory

Hongguang Liu, Karim Noui, Edward Wilson-Ewing, David Langlois
(Submitted on 31 Mar 2017)
Recently, Chamseddine and Mukhanov introduced a higher-derivative scalar-tensor theory which leads to a modified Friedmann equation allowing for bouncing solutions. As we note in the present work, this Friedmann equation turns out to reproduce exactly the loop quantum cosmology effective dynamics for a flat isotropic and homogeneous space-time. We generalize this result to obtain a class of scalar-tensor theories, belonging to the family of mimetic gravity, which all reproduce the loop quantum cosmology effective dynamics for flat, closed and open isotropic and homogeneous space-times.
Comments: 19 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1703.10812 [gr-qc]
On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity
Norbert Bodendorfer, Andreas Schäfer, John Schliemann
(Submitted on 30 Mar 2017)
Chamseddine and Mukhanov recently proposed a modified version of general relativity that implements the idea of a limiting curvature. In the spatially flat, homogeneous, and isotropic sector, their theory turns out to agree with the effective dynamics of the simplest version of loop quantum gravity if one identifies their limiting curvature with a multiple of the Planck curvature. At the same time, it extends to full general relativity without any symmetry assumptions and thus provides an ideal toy model for full loop quantum gravity in the form of a generally covariant effective action known to all orders. In this paper, we study the canonical structure of this theory and point out some interesting lessons for loop quantum gravity. We also highlight in detail how the two theories are connected in the spatially flat, homogeneous, and isotropic sector.
Comments: 12 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1703.10670 [gr-qc]
(or arXiv:1703.10670v1 [gr-qc] for this version)
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]


Science Advisor
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.

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.

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.
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Science Advisor
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.


Science Advisor
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.
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)
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 Schwarszchild 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]
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)


Science Advisor
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.

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 possess 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.


Science Advisor
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.


Science Advisor
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.


Science Advisor
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.

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.

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.

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.

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.

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.


Science Advisor
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.

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.

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.
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)
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
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)
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)

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