http://arxiv.org/abs/1406.7304
Entanglement entropy and nonabelian gauge symmetry
William Donnelly
(Submitted on 27 Jun 2014)
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.
12 pages. Invited article for
Classical and Quantum Gravity special issue on Entanglement and Quantum Gravity
http://arxiv.org/abs/1406.6021
Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity
Jibril Ben Achour, Amaury Mouchet, Karim Noui
(Submitted on 23 Jun 2014)
We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter γ. This construction deeply relies on the link between black holes and Chern-Simons theory. Technically, the key point consists in writing the number of microstates as an integral in the complex plane of a holomorphic function, and to make use of complex analysis techniques to perform the analytic continuation. Then, we study the thermodynamical properties of the corresponding system (the black hole is viewed as a gas of indistinguishable punctures) in the framework of the grand canonical ensemble where the energy is defined à la Frodden-Gosh-Perez from the point of view of an observer located close to the horizon. The semi-classical limit occurs at the Unruh temperature T
U associated to this local observer. When γ=±i, the entropy reproduces at the semi-classical limit the area law with quantum corrections. Furthermore, the quantum corrections are logarithmic provided that the chemical potential is fixed to the simple value μ=2T
U.
31 pages, 2 figures.
http://arxiv.org/abs/1406.3706
Our Universe from the cosmological constant
Aurelien Barrau, Linda Linsefors
(Submitted on 14 Jun 2014)
In this article, we consider a bouncing Universe, as described for example by Loop Quantum Cosmology. If the current acceleration is due to a true cosmological constant, this constant is naturally conserved through the bounce and the Universe should also be in a (contracting) de Sitter phase in the remote past. We investigate here the possibility that the de Sitter temperature in the contracting branch fills the Universe with radiation and causes the bounce and the subsequent inflation and reheating. We also consider the possibility that this gives rise to a cyclic model of the Universe and suggest some possible tests.
5 pages.
http://arxiv.org/abs/1406.2611
Positive energy in quantum gravity
Lee Smolin
(Submitted on 10 Jun 2014)
This paper addresses the question of whether Witten's proof of positive ADM energy for classical general relativity can be extended to give a proof of positive energy for a non-perturbative quantization of general relativity. To address this question, a set of conditions is shown to be sufficient for showing the positivity of a Hamiltonian operator corresponding to the ADM energy. One of these conditions is a particular factor ordering for the constraints of general relativity, in a representation where the states are functionals of the Ashtekar connection, and the auxiliary, Witten spinor.
These developments are partly based on results derived with Artem Starodubtsev (unpublished notes, 2004).
14 pages.
http://arxiv.org/abs/1406.2610
Emergence of string-like physics from Lorentz invariance in loop quantum gravity
Rodolfo Gambini, Jorge Pullin
(Submitted on 10 Jun 2014)
We consider a quantum field theory on a spherically symmetric quantum space time described by loop quantum gravity. The spin network description of space time in such a theory leads to equations for the quantum field that are discrete. We show that to avoid significant violations of Lorentz invariance one needs to consider specific non-local interactions in the quantum field theory similar to those that appear in string theory. This is the first sign that loop quantum gravity places restrictions on the type of matter considered, and points to a connection with string theory physics.
7 pages. Honorable mention Gravity Research Foundation 2014.
http://arxiv.org/abs/1406.1486
Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology
Peter Diener, Brajesh Gupt, Miguel Megevand, Parampreet Singh
(Submitted on 5 Jun 2014)
In recent years, numerical simulations with Gaussian initial states have demonstrated the existence of a quantum bounce in loop quantum cosmology in various models. A key issue pertaining to the robustness of the bounce and the associated physics is to understand the quantum evolution for more general initial states which may depart significantly from Gaussianity and may have no well defined peakedness properties. The analysis of such states, including squeezed and highly non-Gaussian states, has been computationally challenging until now. In this manuscript, we overcome these challenges by using the Chimera scheme for the spatially flat, homogeneous and isotropic model sourced with a massless scalar field. We demonstrate that the quantum bounce in loop quantum cosmology occurs even for states which are highly squeezed or are non-Gaussian with multiple peaks and with little resemblance to semi-classical states. The existence of the bounce is found to be robust, and does not depend on the properties of the states. The evolution of squeezed and non-Gaussian states turns out to be qualitatively similar to the Gaussian states and satisfies strong constraints on the growth of the relative fluctuations across the bounce. We also compare the results from the effective dynamics and find that, though it captures the qualitative aspects of the evolution for squeezed and highly non-Gaussian states, it always underestimates the bounce volume. We show that various properties of the evolution, such as the energy density at the bounce, are in excellent agreement with the predictions from an exactly solvable loop quantum cosmological model for arbitrary states.
26 pages, 16 figures.
http://arxiv.org/abs/1406.0579
The Koslowski-Sahlmann representation: Quantum Configuration Space
Miguel Campiglia, Madhavan Varadarajan
(Submitted on 3 Jun 2014)
The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of Loop Quantum Gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as "background exponentials".
Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones:
(i) the abelian ∗ algebra of SU(2) holonomies and 'U(1)' background exponentials can be completed to a C* algebra
(ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra
(iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum
(iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1)
(v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras.
While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.
33 pages.
http://arxiv.org/abs/1406.0369
Viability of the matter bounce scenario in Loop Quantum Cosmology for general potentials
Jaume Haro, Jaume Amorós
(Submitted on 2 Jun 2014)
We consider the matter bounce scenario in Loop Quantum Cosmology (LQC) for physical potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these models, numerically solving the dynamical equations we have seen that the teleparallel version of LQC leads to theoretical results that fit well with current observational data. More precisely, in teleparallel LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Planck's experimental data. On the other hand, in holonomy corrected LQC the theoretical value of the tensor/scalar ratio is smaller than in teleparallel LQC, which means that there is always a set of solutions that matches with Planck's data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.
29 pages, 8 figures.
http://arxiv.org/abs/1405.7287
Statistical and entanglement entropy for black holes in quantum geometry
Alejandro Perez
(Submitted on 28 May 2014)
We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the relevant degrees of freedom are identified, the two notions coincide. The key ingredient linking the two notions is the structure of quantum geometry at Planck scale implied by loop quantum gravity, where correlations between the inside and outside of the black hole are mediated by eigenstates of the horizon area operator.
11 pages, 3 figures.
http://arxiv.org/abs/1405.5235
Last gasp of a black hole: unitary evaporation implies non-monotonic mass loss
Eugenio Bianchi, Matteo Smerlak
(Submitted on 16 May 2014)
We show within the usual two-dimensional approximation that unitarity and the restoration of Minkowski vacuum correlations at the end of black hole evaporation impose unexpected constraints on its mass loss rate: before disappearing the black hole emits one or more negative energy burst, leading to a temporary increase of its mass.
8 pages; nontechnical version of
http://arxiv.org/abs/1404.0602 E. Bianchi, M.Smerlak
"Entanglement entropy and negative-energy fluxes in two-dimensional space times"
http://arxiv.org/abs/1405.4881
Non-equilibrium thermodynamics of gravitational screens
Laurent Freidel, Yuki Yokokura
(Submitted on 19 May 2014)
We study the Einstein gravity equations projected on a timelike surface, which represents the time evolution of what we call a gravitational screen. We show that such a screen possesses a surface tension and an internal energy, and that the Einstein equations reduce to the thermodynamic equations of a viscous bubble. We also provide a complete dictionary between gravitational and thermodynamical variables. In the non-viscous cases there are three thermodynamic equations which characterise a bubble dynamics: These are the first law, the Marangoni flow equation and the Young-Laplace equation. In all three equations the surface tension plays a central role: In the first law it appears as a work term per unit area, in the Marangoni flow its gradient drives a force, and in the Young-Laplace equation it contributes to a pressure proportional to the surface curvature. The gravity equations appear as a natural generalization of these bubble equations when the bubble itself is viscous and dynamical. In particular, it shows that the mechanism of entropy production for the viscous bubble is mapped onto the production of gravitational waves. We also review the relationship between surface tension and temperature, and discuss the usual black-hole thermodynamics from this point of view.
27 pages, 3 figures.
http://arxiv.org/abs/1405.4585
Renormalization Group Flow in CDT
J. Ambjorn, A. Goerlich, J. Jurkiewicz, A. Kreienbuehl, R. Loll
(Submitted on 19 May 2014)
We perform a first investigation of the coupling constant flow of the nonperturbative lattice model of four-dimensional quantum gravity given in terms of Causal Dynamical Triangulations (CDT). After explaining how standard concepts of lattice field theory can be adapted to the case of this background-independent theory, we define a notion of "lines of constant physics" in coupling constant space in terms of certain semiclassical properties of the dynamically generated quantum universe. Determining flow lines with the help of Monte Carlo simulations, we find that the second-order phase transition line present in this theory can be interpreted as a UV phase transition line if we allow for an anisotropic scaling of space and time.
20 pages
http://arxiv.org/abs/arXiv:1405.1753
Exhaustive investigation of the duration of inflation in effective anisotropic loop quantum cosmology
Linda Linsefors, Aurelien Barrau
(Submitted on 7 May 2014)
This article addresses the issue of estimating the duration in inflation in bouncing cosmology when anisotropies, inevitably playing and important role, are taken into account. It is shown that in Bianchi-I loop quantum cosmology, the higher the shear, the shorter the period of inflation. For a wide range of parameters, the probability distribution function of the duration of inflation is however peaked at values compatible with data, but not much higher. This makes the whole bounce/inflationary scenario consistent and phenomenologically appealing as all the information from the bounce might then not have been fully washed out.
7pages, 5 figures.
http://arxiv.org/abs/1404.5821
Planck star phenomenology
Aurelien Barrau, Carlo Rovelli
(Submitted on 23 Apr 2014)
It is possible that black holes hide a core of Planckian density, sustained by quantum-gravitational pressure. As a black hole evaporates, the core remembers the initial mass and the final explosion occurs at macroscopic scale. We investigate possible phenomenological consequences of this idea. Under several rough assumptions, we estimate that up to several short gamma-ray bursts per day, around 10 MeV, with isotropic distribution, can be expected coming from a region of a few hundred light years around us.
5 pages, 4 figures.
http://arxiv.org/abs/1404.4167
Loop quantum gravity, twistors, and some perspectives on the problem of time
Simone Speziale
(Submitted on 16 Apr 2014)
I give a brief introduction to the relation between loop quantum gravity and twistor theory, and comment on some perspectives on the problem of time.
10 pages, invited lecture to the "2nd International Conference on New Frontiers in Physics 2013" (ICNFP 2013), to be published in EPJ Web of Conferences vol. 71
http://arxiv.org/abs/1404.4036
Loop quantum cosmology of a radiation-dominated flat FLRW universe
Tomasz Pawlowski, Roberto Pierini, Edward Wilson-Ewing
(Submitted on 15 Apr 2014)
We study the loop quantum cosmology of a flat Friedmann-Lemaitre-Robertson-Walker space-time with a Maxwell field. We show that many of the qualitative properties derived for the case of a massless scalar field also hold for a Maxwell field. In particular, the big-bang singularity is replaced by a quantum bounce, and the operator corresponding to the matter energy density is bounded above by the same critical energy density. We also numerically study the evolution of wave functions that are sharply peaked in the low energy regime, and derive effective equations which very closely approximate the full quantum dynamics of sharply peaked states at all times, including the near-bounce epoch.
27 pages, 6 figures.
http://arxiv.org/abs/1404.2944
Quantum cosmology of (loop) quantum gravity condensates: An example
Steffen Gielen
(Submitted on 10 Apr 2014)
Spatially homogeneous universes can be described in (loop) quantum gravity as condensates of elementary excitations of space. Their treatment is easiest in the second-quantised group field theory formalism which allows the adaptation of techniques from the description of Bose-Einstein condensates in condensed matter physics. Dynamical equations for the states can be derived directly from the underlying quantum gravity dynamics. The analogue of the Gross-Pitaevskii equation defines an anisotropic quantum cosmology model, in which the condensate wavefunction becomes a quantum cosmology wavefunction on minisuperspace. To illustrate this general formalism, we give a mapping of the gauge-invariant geometric data for a tetrahedron to a minisuperspace of homogeneous anisotropic 3-metrics. We then study an example for which we give the resulting quantum cosmology model in the general anisotropic case and derive the general analytical solution for isotropic universes. We discuss the interpretation of these solutions and comment on the validity of the WKB approximation used in previous studies.
20 pages, 2 figures.
http://arxiv.org/abs/1404.2284
Cosmological Constant from the Emergent Gravity Perspective
T. Padmanabhan, Hamsa Padmanabhan
(Submitted on 8 Apr 2014)
Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant Λ, with the dimensionless parameter ΛL
P2 ≃ 10
−122, where L
P=(Gℏ/c
3)
1/2 is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which
(i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and
(ii) the cosmological constant appears as an integration constant in the solution.
The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value 4π, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.
48 pages; 5 figures. Invited review to appear in
Int. Jour. Mod. Phys. D
http://arxiv.org/abs/1404.1750
How many quanta are there in a quantum spacetime?
Seramika Ariwahjoedi, Jusak Sali Kosasih, Carlo Rovelli, Freddy P. Zen
(Submitted on 7 Apr 2014)
Following earlier insights by Livine and Terno, we develop a technique for describing quantum states of the gravitational field in terms of coarse grained spin networks. We show that the number of nodes and links and the values of the spin depend on the observables chosen for the description of the state. Hence the question in the title of this paper is ill posed, unless further information about what is being measured is given.
16 pages, 9 figures.
http://arxiv.org/abs/1403.6457
Purity is not eternal at the Planck scale
Michele Arzano
(Submitted on 25 Mar 2014)
Theories with Planck-scale deformed symmetries exhibit quantum time evolution in which purity of the density matrix is not preserved. In particular we show that the non-trivial structure of momentum space of these models is reflected in a deformed action of translation generators on operators. Such action in the case of time translation generators leads to a Lindblad-like evolution equation for density matrices when expanded at leading order in the Planckian deformation parameter. This evolution equation is covariant under the deformed realization of Lorentz symmetries characterizing these models.
6 pages.