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marcus

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## Main Question or Discussion Point

The fourth quarter 2013 has already seen an interesting bunch of Loop gravity research papers. I'll list a few and say why I think they are remarkable. Some make meaningful progress along established lines, while one or more others take an unexpected direction and are clearly exceptional. Highlights in the authors' abstracts are in blue, my comments on why the paper seems especially important are in green.

http://arxiv.org/abs/1310.5996

Rodolfo Gambini, Javier Olmedo, Jorge Pullin

(Submitted on 22 Oct 2013)

We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.

20 pages

Progress in showing that the Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

http://arxiv.org/abs/1310.4795

Peter Diener, Brajesh Gupt, Parampreet Singh

(Submitted on 17 Oct 2013)

The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.

39 pages, 15 figures

Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes further generalization possible.

http://arxiv.org/abs/1310.3362

Etera R. Livine

(Submitted on 12 Oct 2013)

In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.

24 pages

The paper explains a new coarsegrain proceedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

http://arxiv.org/abs/1310.2174

Aldo Riello

(Submitted on 8 Oct 2013)

I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.

13 pages, 4 figures

Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

http://arxiv.org/abs/1310.1290

Paula Tarrío, Mikel Fernández Méndez, Guillermo A. Mena Marugán

(Submitted on 4 Oct 2013)

One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in Loop Quantum Cosmology including inhomogeneities and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the homogeneous case.

11 pages, 2 figures

Important to relax the requirement of inhomogeneity and extend the cosmological Big Bounce result to increasingly general cases.

http://arxiv.org/abs/1310.5996

**Quantum black holes in Loop Quantum Gravity**Rodolfo Gambini, Javier Olmedo, Jorge Pullin

(Submitted on 22 Oct 2013)

We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.

20 pages

Progress in showing that the Loop black hole does not develop a singularity. The authors published a result earlier this year in PRL which is now strengthened by showing that when one takes an alternate quantization route it again goes through and gives equivalent physics.

http://arxiv.org/abs/1310.4795

**Chimera: A hybrid approach to numerical loop quantum cosmology**Peter Diener, Brajesh Gupt, Parampreet Singh

(Submitted on 17 Oct 2013)

The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.

39 pages, 15 figures

Computer simulations of have played an important role in Loop cosmology especially since 2006---having been extensively used to check and confirm solvable equation models and verify the Big Bounce under increasingly general assumptions. More efficient code makes further generalization possible.

http://arxiv.org/abs/1310.3362

**Deformation Operators of Spin Networks and Coarse-Graining**Etera R. Livine

(Submitted on 12 Oct 2013)

In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop gravity, a necessary step is to understand the coarse-graining of these states in order to describe their relevant structure at various scales. Using the spinor network formalism to describe the phase space of loop gravity on a given graph, we focus on a bounded (connected) region of the graph and coarse-grain it to a single vertex using a gauge-fixing procedure. We discuss the ambiguities in the gauge-fixing procedure and their consequences for coarse-graining spin(or) networks. This allows to define the boundary deformations of that region in a gauge-invariant fashion and to identify the area preserving deformations as U(N) transformations similarly to the already well-studied case of a single intertwiner. The novelty is that the closure constraint is now relaxed and the closure defect interpreted as a local measure of the curvature inside the coarse-grained region. It is nevertheless possible to cancel the closure defect by a Lorentz boost. We further identify a Lorentz-invariant observable related to the area and closure defect, which we name "rest area". Its physical meaning remains an open issue.

24 pages

The paper explains a new coarsegrain proceedure to collapse a compact region of a spin(or) network with multiple vertices and edges down to a single point. A Fock-style Hilbert space is constructed at the remaining vertex which represents information condensed by the coarsening move. The reverse process of refinement is studied.

http://arxiv.org/abs/1310.2174

**Radiative corrections to the EPRL-FK spinfoam graviton**Aldo Riello

(Submitted on 8 Oct 2013)

I study the corrections engendered by the insertion of a "melon" graph in the bulk of the first-order spinfoam used for the graviton propagator. I find that these corrections are highly non-trivial and, in particular, that they concern those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of vanishing Barbero-Immirzi parameter at fixed area. This fact is the first realization of the often cited idea that the spinfoam amplitude receives higher order corrections under the refinement of the underlying two-complex.

13 pages, 4 figures

Riello's earlier paper this year dealt with spinfoam amplitude divergences which turned out to be at most logarithmic. He continues to make headway in studying details of the covariant Loop gravity path integral under refinement

http://arxiv.org/abs/1310.1290

**Singularity avoidance in the hybrid quantization of the Gowdy model**Paula Tarrío, Mikel Fernández Méndez, Guillermo A. Mena Marugán

(Submitted on 4 Oct 2013)

One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in Loop Quantum Cosmology including inhomogeneities and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the homogeneous case.

11 pages, 2 figures

Important to relax the requirement of inhomogeneity and extend the cosmological Big Bounce result to increasingly general cases.