http://arxiv.org/abs/1309.7296
Astrophysical constraints on Planck scale dissipative phenomena
Stefano Liberati (SISSA and INFN, Trieste), Luca Maccione (LMU and MPP, Munich)
(Submitted on 27 Sep 2013)
The emergence of a classical spacetime from any quantum gravity model is still a subtle and only partially understood issue. If indeed space-time is arising as some sort of large scale condensate of more fundamental objects then it is natural to expect that matter, being a collective excitations of the spacetime constituents, will present modified kinematics at sufficiently high energies. We consider here the phenomenology of the dissipative effects necessarily arising in such a picture. Adopting dissipative hydrodynamics as a general framework for the description of the energy exchange between collective excitations and the spacetime fundamental degrees of freedom, we discuss how rates of decays for elementary particles can be derived from dispersion relations and used to provide strong constraints on the base of current astrophysical observations of high energy particles.
5 pages, 1 figure
http://arxiv.org/abs/1309.7273
Renormalization group flow of Hořava-Lifshitz gravity at low energies
Adriano Contillo, Stefan Rechenberger, Frank Saueressig
(Submitted on 27 Sep 2013)
The functional renormalization group equation for projectable Horava-Lifshitz gravity is used to derive the non-perturbative beta functions for the Newton's constant, cosmological constant and anisotropy parameter. The resulting coupled differential equations are studied in detail and exemplary RG trajectories are constructed numerically. The beta functions possesses a non-Gaussian fixed point and a one-parameter family of Gaussian fixed points. One of the Gaussian fixed points corresponds to the Einstein-Hilbert action with vanishing cosmological constant and constitutes a saddle point with one IR-attractive direction. For RG trajectories dragged into this fixed point at low energies diffeomorphism invariance is restored. The emergence of general relativity from Horava-Lifshitz gravity can thus be understood as a crossover-phenomenon where the IR behavior of the theory is controlled by this Gaussian fixed point. In particular RG trajectories with a tiny positive cosmological constant also come with an anisotropy parameter which is compatible with experimental constraints, providing a mechanism for the approximate restoration of diffeomorphism invariance in the IR. The non-Gaussian fixed point is UV-attractive in all three coupling constants. Most likely, this fixed point is the imprint of Asymptotic Safety at the level of Horava-Lifshitz gravity.
32 pages, 6 figures
http://arxiv.org/abs/1309.6896
Observational issues in loop quantum cosmology
A. Barrau, T. Cailleteau, J. Grain, J. Mielczarek
(Submitted on 26 Sep 2013)
Quantum gravity is sometimes considered as a kind of metaphysical speculation. In this review, we show that, although still extremely difficult to reach, observational signatures can in fact be expected. The early universe is an invaluable laboratory to probe "Planck scale physics". Focusing on Loop Quantum Gravity as one of the best candidate for a non-perturbative and background-independant quantization of gravity, we detail some expected features.
75 pages, invited topical review for Classical and Quantum Gravity
http://arxiv.org/abs/1309.6304
Quantum-Reduced Loop-Gravity: Relation with the Full Theory
Emanuele Alesci, Francesco Cianfrani, Carlo Rovelli
(Submitted on 24 Sep 2013)
The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects states based on reduced graphs with Livine-Speziale coherent intertwiners and could simplify the analysis of the dynamics in the full theory.
5 pages
http://arxiv.org/abs/1309.4563
Statistics, holography, and black hole entropy in loop quantum gravity
Amit Ghosh, Karim Noui, Alejandro Perez
(Submitted on 18 Sep 2013)
In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or
punctures) labelled by spin j. The excitations possibly carry other internal degrees of freedom also, and the associated quantum states are eigenstates of the area A operator. On the other hand, the appropriately scaled area operator A/(8π ℓ) is also the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance l from the horizon. Thus, the local energy is entirely accounted for by the geometric operator A.
We assume that: In a suitable vacuum state with regular energy momentum tensor at and close to the horizon the local temperature measured by stationary observers is the Unruh temperature and the degeneracy of 'matter' states is exponential with the area exp(λ A/ ℓ
p2) -- this is supported by the well established results of QFT in curved spacetimes, which do not determine λ but asserts an exponential behaviour. The geometric excitations of the horizon (punctures) are indistinguishable. In the semiclassical limit the area of the black hole horizon is large in Planck units.
It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound,
viz. λ = 1/4. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy S= A/(4ℓ
p2) The number of horizon punctures goes like N ~ sqrt(A/ℓ
p2) , i.e the number of punctures N remains large in the semiclassical limit. Fluctuations of the horizon area are small while fluctuations of the area of an individual puncture are large. A precise notion of local conformal invariance of the thermal state is recovered in the A → ∞ limit where the near horizon geometry becomes Rindler.
26 pages
http://arxiv.org/abs/1309.0777
Coupling and thermal equilibrium in general-covariant systems
Goffredo Chirco, Hal M. Haggard, Carlo Rovelli
(Submitted on 3 Sep 2013)
A fully general-covariant formulation of statistical mechanics is still lacking. We take a step toward this theory by studying the meaning of statistical equilibrium for coupled, parametrized systems. We discuss how to couple parametrized systems. We express the thermalization hypothesis in a general-covariant context. This takes the form of vanishing of information flux. An interesting relation emerges between thermal equilibrium and gauge.
8 pages, 3 figures
http://arxiv.org/abs/1309.0311
Phenomenology of Space-time Imperfection I: Nonlocal Defects
Sabine Hossenfelder
(Submitted on 2 Sep 2013)
If space-time is emergent from a fundamentally non-geometric theory it will generically be left with defects. Such defects need not respect the locality that emerges with the background. Here, we develop a phenomenological model that parameterizes the effects of nonlocal defects on the propagation of particles. In this model, Lorentz-invariance is preserved on the average. We derive constraints on the density of defects from various experiments.
25 pages, 7 figures
http://arxiv.org/abs/1309.0314
Phenomenology of Space-time Imperfection II: Local Defects
Sabine Hossenfelder
(Submitted on 2 Sep 2013)
We propose a phenomenological model for the scattering of particles on space-time defects in a treatment that maintains Lorentz-invariance on the average. The local defects considered here cause a stochastic violation of momentum conservation. The scattering probability is parameterized in the density of defects and the distribution of the momentum that a particle can obtain when scattering on the defect. We identify the most promising observable consequences and derive constraints from existing data.
18 pages, 5 figures
http://arxiv.org/abs/1308.4348
The Echo of the Quantum Bounce
Luis J. Garay, Mercedes Martin-Benito, Eduardo Martin-Martinez
(Submitted on 20 Aug 2013)
We identify a signature of quantum gravitational effects that survives from the early universe to the current era: Fluctuations of quantum fields as seen by comoving observers are significantly influenced by the history of the early universe. In particular we will show how the existence (or not) of a quantum bounce leaves a trace in the background quantum noise that is not damped and would be non-negligible even nowadays. Furthermore, we will estimate an upper bound to the typical energy and length scales where quantum effects are relevant. We will discuss how this signature might be observed and therefore used to build falsifiability tests of quantum gravity theories.
5 pages, 3 figures
http://arxiv.org/abs/1308.4063
Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity
Muxin Han
(Submitted on 19 Aug 2013)
A low-energy perturbation theory is developed from the nonperturbative framework of covariant Loop Quantum Gravity (LQG) by employing the background field method. The resulting perturbation theory is a 2-parameter expansion in the semiclassical and low-energy regime. The two expansion parameters are the large spin and small curvature. The leading order effective action coincides with the Einstein-Hilbert action. The subleading corrections organized by the two expansion parameters give the modifications of Einstein gravity in quantum and high-energy regime from LQG. The result of the paper may be viewed as the first step toward understanding the UV completeness of LQG.
5 pages, 1 figure
http://arxiv.org/abs/1308.2946
Purely geometric path integral for spin foams
Atousa Chaharsough Shirazi, Jonathan Engle
(Submitted on 13 Aug 2013)
Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of histories it is important that the integrand have not only the correct phase -- a topic of recent focus in spin-foams -- but also the correct modulus, usually referred to as the measure factor. The correct measure factor descends from the Liouville measure on the reduced phase space, and its calculation is a task of canonical analysis.
The covariant formulation of gravity from which spin-foams are derived is the Plebanski-Holst formulation, in which the basic variables are a Lorentz connection and a Lorentz-algebra valued two-form, called the Plebanski two-form. However, in the final spin-foam sum, one sums over only spins and intertwiners, which label eigenstates of the Plebanski two-form alone. The spin-foam sum is therefore a discretized version of a Plebanski-Holst path integral in which only the Plebanski two-form appears, and in which the connection degrees of freedom have been integrated out. We call this a purely geometric Plebanski-Holst path integral.
In prior work in which one of the authors was involved, the measure factor for the Plebanski-Holst path integral with both connection and two-form variables was calculated. Before one discretizes this measure and incorporates it into a spin-foam sum, however, one must integrate out the connection in order to obtain the purely geometric version of the path integral. To calculate this purely geometric path integral is the principal task of the present paper, and it is done in two independent ways. Gauge-fixing and the background independence of the resulting path integral are discussed in the appendices.
21 pages
http://arxiv.org/abs/1308.2934
The Fundamental Group of a Spatial Section Represented by a Topspin Network
Christopher L Duston
(Submitted on 13 Aug 2013)
We present an algorithm which determines the fundamental group of a spatial section using topspin networks. Tracking the topology of the spatial section is a unique feature of this approach, which is not possible in standard Loop Quantum Gravity. This leads to an example of spatial topology change in a smooth 4-manifold represented by a topspin foam.
7 pages. Based on work presented at the LOOPS 13 conference at the Perimeter Institute
http://arxiv.org/abs/1308.2206
Energetic Causal Sets
Marina Cortês, Lee Smolin
(Submitted on 9 Aug 2013)
We propose an approach to quantum theory based on the energetic causal sets, introduced in Cortês and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no hbar. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level.
9 pages. Article companion to
http://arxiv.org/abs/1307.6167
http://arxiv.org/abs/1308.0687
Anisotropic Spinfoam Cosmology
Julian Rennert, David Sloan
(Submitted on 3 Aug 2013)
The dynamics of a homogeneous, anisotropic universe are investigated within the context of spinfoam cosmology. Transition amplitudes are calculated for a graph consisting of a single node and three links - the `Daisy graph' - probing the behaviour a classical Bianchi I spacetime. It is shown further how the use of such single node graphs gives rise to a simplification of states such that all orders in the spin expansion can be calculated, indicating that it is the vertex expansion that contains information about quantum dynamics.
28 pages, 1 figure
http://arxiv.org/abs/1308.0040
Spinning geometry = Twisted geometry
Laurent Freidel, Jonathan Ziprick
(Submitted on 31 Jul 2013)
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies.
We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space.
20 pages, 5 figures
http://arxiv.org/abs/1307.5885
Linking covariant and canonical LQG II: Spin foam projector
Thomas Thiemann, Antonia Zipfel
(Submitted on 22 Jul 2013)
In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time extended the definition of spin foam models to arbitrary boundary graphs. This is a prerequisite in order to make contact to the canonical formulation of Loop Quantum Gravity (LQG) and allows to investigate the question whether any of the presently considered spin foam models yield a rigging map for any of the presently defined Hamiltonian constraint operators. The KKL extension cannot be described in terms of Group Field Theory (GFT) since arbitrary foams are involved while GFT is tied to simplicial complexes. Therefore one has to define the sum over spin foams with given boundary spin networks in an independent fashion using natural axioms, most importantly a gluing property for 2-complexes. These axioms are motivated by the requirement that spin foam amplitudes should define a rigging map (physical inner product) induced by the Hamiltonian constraint. This is achieved by constructing a spin foam operator based on abstract 2-complexes that acts on the kinematical Hilbert space of Loop Quantum Gravity. In the analysis of the resulting object we are able to identify an elementary spin foam transfer matrix that allows to generate any finite foam as a finite power of the transfer matrix. It transpires that the sum over spin foams, as written, does not define a projector on the physical Hilbert space. This statement is independent of the concrete spin foam model and Hamiltonian constraint. However, the transfer matrix potentially contains the necessary ingredient in order to construct a proper rigging map in terms of a modified transfer matrix.
62 pages, 14 figures
http://arxiv.org/abs/1307.5469
De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
S. Jordan, R. Loll
(Submitted on 20 Jul 2013)
We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and causal properties, present details of the numerical set-up and explain how to extract "volume profiles". Extensive Monte Carlo measurements of the system show the emergence of a de Sitter universe on large scales from the underlying quantum ensemble, similar to what was observed previously in standard CDT quantum gravity. This provides evidence that the distinguished time slicing of the latter is not an essential part of its kinematical set-up.
44 pages, 29 figures
http://arxiv.org/abs/1307.5238
Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology
Thomas Cailleteau, Linda Linsefors, Aurelien Barrau
(Submitted on 19 Jul 2013)
This article addresses the issue of the closure of the algebra of constraints for generic (cosmological) perturbations when taking into account simultaneously the two main corrections of effective loop quantum cosmology, namely the holonomy and the inverse-volume terms. Previous works on either the holonomy or the inverse volume case are reviewed and generalized. In the inverse-volume case, we point out new possibilities. An anomaly-free solution including both corrections is found for perturbations, and the corresponding equations of motion are derived.
19 pages.
http://arxiv.org/abs/1307.5029
Black hole entropy from loop quantum gravity in higher dimensions
Norbert Bodendorfer
(Submitted on 18 Jul 2013)
We propose a derivation for computing black hole entropy for spherical non-rotating isolated horizons from loop quantum gravity in four and higher dimensions. The state counting problem effectively reduces to the well studied 3+1-dimensional one based on an SU(2)-Chern-Simons theory, differing only in the precise form of the area spectrum and the restriction to integer spins.
5 pages
http://arxiv.org/abs/1307.3228
Maximal acceleration in covariant loop gravity and singularity resolution
Carlo Rovelli, Francesca Vidotto
(Submitted on 11 Jul 2013)
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
4 pages, 1 figure