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Loop-and-allied QG bibliography

  1. Nov 19, 2017 #2541


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    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.

    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.

    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.

    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.

    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.

    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.

    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.

    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.

    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.

    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.

    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.

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

    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.

    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.

    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.

    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 #2542


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    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.


    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.

    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.

    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.

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