# Loop-and-allied QG bibliography

1. Nov 19, 2017

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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
(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.

Last edited: Nov 20, 2017
2. Dec 3, 2017

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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.

Last edited: Feb 18, 2018
3. Dec 23, 2017

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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.

4. Feb 3, 2018

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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.

Last edited: Feb 17, 2018
5. Feb 17, 2018

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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.

6. Mar 11, 2018

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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
(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 possess 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.

Last edited: Mar 11, 2018
7. Mar 29, 2018

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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.

8. Apr 4, 2018

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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.

9. Apr 10, 2018

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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.

10. Jul 13, 2018

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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 realise 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
(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.

11. Aug 17, 2018 at 9:06 AM

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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
(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.