http://arxiv.org/abs/1303.7216
Relative Locality in Curved Space-time
Jerzy Kowalski-Glikman, Giacomo Rosati
(Submitted on 28 Mar 2013)
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are presents. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with kappa-Poincaré momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.
8 pages
http://arxiv.org/abs/1303.7139
Symmetry and Evolution in Quantum Gravity
Sean Gryb, Karim Thebault
(Submitted on 28 Mar 2013)
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory makes predictions that are distinct from Wheeler-DeWitt cosmology. Furthermore, the local symmetry principle - and corresponding observables - of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.
36 preprint pages. 1 table
http://arxiv.org/abs/1303.6157
Loop quantum dynamics of the gravitational collapse
Yaser Tavakoli, Joao Marto, Andrea Dapor
(Submitted on 25 Mar 2013)
We consider a quantum description for a spherically symmetric gravitational collapse of a massless scalar field. The effective scenario from loop quantum gravity is applied to a homogeneous interior spacetime. The classical singularity that arises at the final stage of our collapsing system is resolved and replaced by a quantum bounce. Our main purpose is to investigate the evolution of trapped surfaces during the collapse in semiclassical regime. We show that, in this regime, there exists a threshold scale below which no horizon can form as collapse evolves towards the bounce. By employing the matching conditions at the boundary shell, quantum effects are carried out to the exterior region, leading to an improved Vaidya geometry. In addition, the effective mass loss emerging in this model predicts an outward energy flux from the interior quantum geometry regime.
11 pages, 5 figures
http://arxiv.org/abs/1303.5612
A Gravitational Entropy Proposal
Timothy Clifton, George F R Ellis, Reza Tavakol
(Submitted on 22 Mar 2013)
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel-Robinson tensor, which has a natural interpretation as the effective super-energy-momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein-Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson-Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein's field equations. It is also in keeping with Penrose's Weyl curvature hypothesis.
17 pages
http://arxiv.org/abs/1303.4989
Loop Quantum Gravity and the The Planck Regime of Cosmology
Abhay Ashtekar
(Submitted on 20 Mar 2013)
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects, such as a modification of the consistency relation involving the scalar and tensor power spectra and a new source for non-Gaussianities. Thus, the genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations in the Planck regime. This report provides a bird's eye view of these developments for the general relativity community.
23 pages, 4 figures. Plenary talk at the Conference: Relativity and Gravitation: 100 Years after Einstein in Prague. To appear in the Proceedings to be published by Edition Open Access. Summarizes results that appeared in journal articles [2-13]
http://arxiv.org/abs/1303.4752
Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
Norbert Bodendorfer, Yasha Neiman
(Submitted on 19 Mar 2013)
It was recently noted that the on-shell Einstein-Hilbert action with York-Gibbons-Hawking boundary term has an imaginary part, proportional to the area of the codimension-2 surfaces on which the boundary normal becomes null. We extend this result to first-order formulations of gravity, by generalizing a previously proposed boundary term to closed boundaries. As a side effect, we settle the issue of the Holst modification vs. the Nieh-Yan density by demanding a well-defined variational principle. We then set out to find the imaginary action in the large-spin 4-simplex limit of the Lorentzian EPRL/FK spinfoam. It turns out that the spinfoam's effective action indeed has the correct imaginary part, but only if the Barbero-Immirzi parameter γ is set to ± i after the quantum calculation. An interpretation and a connection to other recent results is discussed. In particular, we propose that the large-spin limit of loop quantum gravity can be viewed as a high-energy 'transplanckian' regime.
22 pages, 5 figures
http://arxiv.org/abs/1303.3576
Cosmology from Group Field Theory
Steffen Gielen, Daniele Oriti, Lorenzo Sindoni
(Submitted on 14 Mar 2013)
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a non-linear and non-local extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semi-classical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
5 pages
http://arxiv.org/abs/1303.2773
BTZ Black Hole Entropy in Loop Quantum Gravity and in Spin Foam Models
J.Manuel Garcia-Islas
(Submitted on 12 Mar 2013)
We present a comparison of the calculation of BTZ black hole entropy in loop quantum gravity and in spin foam models. We see that both give the same answer.
6 pages, 3 figures
http://arxiv.org/abs/1303.0752
Inclusion of matter in inhomogeneous loop quantum cosmology
Daniel Martín-de Blas, Mercedes Martín-Benito, Guillermo A. Mena Marugán
(Submitted on 4 Mar 2013)
We study the hybrid quantization of the linearly polarized Gowdy T
3 model with a massless scalar field with the same symmetries as the metric. For simplicity, we quantize its restriction to the model with local rotational symmetry. Using this hybrid approach, the homogeneous degrees of freedom of the geometry are quantized à la loop, leading to the resolution of the cosmological singularity. A Fock quantization is employed both for the matter and the gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat Friedmann-Robertson-Walker cosmologies filled with inhomogeneities propagating in one direction, providing a perfect scenario to study the quantum back-reaction of the inhomogeneities on the polymeric homogeneous and isotropic background.
4 pages
http://arxiv.org/abs/1302.7142
Holonomy Operator and Quantization Ambiguities on Spinor Space
Etera R. Livine
(Submitted on 28 Feb 2013)
We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant 'generalized ladder operators' recently introduced in the U(N) approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity.
14 pages
http://arxiv.org/abs/1302.5265
The loop quantum gravity black hole
Rodolfo Gambini, Jorge Pullin
(Submitted on 21 Feb 2013)
We quantize spherically symmetric vacuum gravity without gauge fixing the diffeomorphism constraint. Through a rescaling, we make the algebra of Hamiltonian constraints Abelian and therefore the constraint algebra is a true Lie algebra. This allows the completion of the Dirac quantization procedure using loop quantum gravity techniques. We can construct explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. New observables living in the bulk appear at the quantum level (analogous to spin in quantum mechanics) that are not present at the classical level and are associated with the discrete nature of the spin network states of loop quantum gravity. The resulting quantum space-times resolve the singularity present in the classical theory inside black holes. The new observables that arise suggest a possible resolution for the "firewall" problem of evaporating black holes.
4 pages
http://arxiv.org/abs/1302.3833
Loop Quantum Cosmology
Ivan Agullo, Alejandro Corichi
(Submitted on 15 Feb 2013)
This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of effective equations that incorporate the main quantum corrections to the dynamics. We also summarize the theory of quantized metric perturbations propagating in those quantum backgrounds. Finally, we describe how this framework can be applied to obtain a self-consistent extension of the inflationary scenario to incorporate quantum aspects of gravity, and to explore possible phenomenological consequences.
52 pages, 5 figures. To appear as a Chapter of "The Springer Handbook of Spacetime," edited by A. Ashtekar and V. Petkov. (Springer-Verlag, at Press).
http://arxiv.org/abs/1302.1781
Self-Energy in the Lorentzian ERPL-FK Spin Foam Model of Quantum Gravity
Aldo Riello
(Submitted on 7 Feb 2013)
We calculate the most divergent contribution to the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK Spin Foam model of Quantum Gravity. We find that such a contribution is logarithmically divergent in the cut-off over the SU(2)-representation spins when one chooses the face amplitude guaranteeing the face-splitting invariance of the foam. We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the non-commutativity of the EPRL-FK Y-map with the projector onto SL(2,C)-invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, its geometrical interpretation as well as the physical consequences of our result.
55 pages, 8 figures
http://arxiv.org/abs/1302.0724
Death and resurrection of the zeroth principle of thermodynamics
Hal M. Haggard, Carlo Rovelli
(Submitted on 4 Feb 2013)
The zeroth principle of thermodynamics in the form "temperature is uniform at equilibrium" is notoriously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of two interacting systems under energy exchanges. Here we discuss a generalized version of this derivation, based on informational notions, which remains valid in the general context. The result is based on the observation that the time taken by any system to move to a distinguishable (nearly orthogonal) quantum state is a universal quantity that depends solely on the temperature. At equilibrium the net information flow between two systems must vanish, and this happens when two systems transit the same number of distinguishable states in the course of their interaction.
5 pages, 2 figures
http://arxiv.org/abs/1302.0254
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 1 Feb 2013)
Using techniques from loop quantum gravity, the standard theory of cosmological perturbations was recently generalized to encompass the Planck era. We now apply this framework to explore pre-inflationary dynamics. The framework enables us to isolate and resolve the true trans-Planckian difficulties, with interesting lessons both for theory and observations. ... departures from the standard paradigm, with novel effects ---such as a modification of the consistency relation between the ratio of the tensor to scalar power spectrum and the tensor spectral index, as well as a new source for non-Gaussianities--- which could extend the reach of cosmological observations to the deep Planck regime of the early universe.
64 pages, 15 figures
http://arxiv.org/abs/1301.6210
Embedding loop quantum cosmology without piecewise linearity
Jonathan Engle
(Submitted on 26 Jan 2013)
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC),
directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, ...The present paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on
piecewise analytic paths. The embedding is well-defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed, and at no point is the piecewise linear category used. ... The construction is made possible by a recent result proven by Fleischhack.
18 pages
http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. ... Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures
http://arxiv.org/abs/1301.3480
Gauge networks in noncommutative geometry
Matilde Marcolli, Walter D. van Suijlekom
(Submitted on 15 Jan 2013)
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. ... gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences.
... we define a discretized Dirac operator on the quiver. We compute the spectral action of this Dirac operator on a four-dimensional lattice, and find that it reduces to the Wilson action for lattice gauge theories and a Higgs field lattice system. As such, in the continuum limit it reduces to the Yang-Mills-Higgs system. ...
30 pages
http://arxiv.org/abs/1301.2245
Quantum-Reduced Loop Gravity: Cosmology
Emanuele Alesci, Francesco Cianfrani
(Submitted on 10 Jan 2013)
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory...The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.
26 pages.
http://arxiv.org/abs/1301.1264
Inflation as a prediction of loop quantum cosmology
Linda Linsefors, Aurelien Barrau
(Submitted on 7 Jan 2013)
Loop quantum cosmology is known to be closely linked with an inflationary phase. In this article, we study quantitatively the probability for a long enough stage of slow-roll inflation to occur, by assuming a minimalist massive scalar field as the main content of the universe. The phase of the field in its "pre-bounce" oscillatory state is taken as a natural random parameter. We find that the probability for a given number of inflationary e-folds is quite sharply peaked around 145, which is indeed more than enough to solve all the standard cosmological problems...
6 pages, 4 figures