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Science Advisor

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**Spin-foam model for gravity coupled to massless scalar field**

Marcin Kisielowski, Jerzy Lewandowski

(Submitted on 16 Jul 2018)

A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.

https://arxiv.org/abs/1807.06354

**Hamiltonian analysis of the BFCG formulation of General Relativity**

Aleksandar Mikovic, Miguel A. Oliveira, Marko Vojinovic

(Submitted on 17 Jul 2018)

We perform the complete Hamiltonian analysis of the BFCG action for General Relativity. We determine all the constraints of the theory and classify them into the first-class and the second-class constraints. We also show how the canonical formulation of BFCG General Relativity reduces to the Einstein-Cartan and triad canonical formulations. The reduced phase space analysis also gives a 2-connection which is suitable for the construction of a spin-foam basis which will be a categorical generalization of the spin-network basis from Loop Quantum Gravity.

https://arxiv.org/abs/1807.06848

**Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners**

Etera R. Livine

(Submitted on 18 Jul 2018)

We describe the Lorentzian version of the Kapovitch-Millson phase space for polyhedra with N faces. Starting with the Schwinger representation of the su(1,1) Lie algebra in terms of a pair of complex variables (or spinor), we define the phase space for a space-like vectors in the three-dimensional Minkowski space R1,2. Considering N copies of this space, quotiented by a closure constraint forcing the sum of those 3-vectors to vanish, we obtain the phase space for Lorentzian polyhedra with N faces whose normal vectors are space-like, up to Lorentz transformations. We identify a generating set of SU(1,1)-invariant observables, whose flow by the Poisson bracket generate both area-preserving and area-changing deformations. We further show that the area-preserving observables form a glN(R) Lie algebra and that they generate a GLN(R) action on Lorentzian polyhedra at fixed total area. That action is cyclic and all Lorentzian polyhedra can be obtained from a totally squashed polyhedron (with only two non-trivial faces) by a GLN(R) transformation. All those features carry on to the quantum level, where quantum Lorentzian polyhedra are defined as SU(1,1) intertwiners between unitary SU(1,1)-representations from the principal continuous series. Those SU(1,1)-intertwiners are the building blocks of spin network states in loop quantum gravity in 3+1 dimensions for time-like slicing and the present analysis applies to deformations of the quantum geometry of time-like boundaries in quantum gravity, which is especially relevant to the study of quasi-local observables and holographic duality.

https://arxiv.org/abs/1807.10704

**Gravitational Fluctuations as an Alternative to Inflation**

Herbert W. Hamber, Lu Heng Sunny Yu

(Submitted on 27 Jul 2018)

In this work we explore an explanation for the galaxy power spectrum P(k) based on the non-perturbative quantum field-theoretical treatment of Einstein gravity, instead of one based on inflation models. In particular the power spectral index, which represents the slope on the P(k) graph, can be related to critical scaling exponents derived from the Wilson renormalization group analysis, and one finds that the derived value fits favorably with the Sloan Digital Sky Survey telescope data. We then make use of the transfer functions, based only on the Boltzmann equations which describe states out of equilibrium, and Einstein's General Relativity, to extrapolate the power spectrum to the Cosmic Microwave Background (CMB) regime and find that the results fits rather well with current data. Our approach contrasts with the conventional explanation which uses inflation to generate the scale invariant Harrison-Zel'dovich spectrum on CMB scales, and uses the transfer function to extrapolate it to galaxy regime. The results we present here only assumes quantum field theory and Einstein's Gravity, and hence provides a competing explanation of the power spectrum, without relying on the assumptions usually associated with inflationary models.

https://arxiv.org/abs/1808.00207

**Quantum fields in the background spacetime of a loop quantum gravity black hole**

Flora Moulin, Killian Martineau, Julien Grain, Aurélien Barrau

(Submitted on 1 Aug 2018)

The description of black holes in loop quantum gravity is a hard and tricky task. In this article, we focus on a minisuperspace approach based on a polymerization procedure. We consider the resulting effective metric and study the propagation of quantum fields in this background. The cross sections for scalar particles and fermions are explicitly calculated. The radial equation of motion is also derived in full generality, beyond the specifically considered metric.

https://arxiv.org/abs/1808.00673

**From Euclidean to Lorentzian Loop Quantum Gravity via a Positive Complexifier**

Madhavan Varadarajan

(Submitted on 2 Aug 2018 (v1), last revised 5 Aug 2018 (this version, v2))

We construct a positive complexifier, differentiable almost everywhere on the classical phase space of real triads and SU(2) connections, which generates a Wick Transform from Euclidean to Lorentzian gravity everywhere except on a phase space set of measure zero. This Wick transform assigns an equal role to the self dual and anti-self dual Ashtekar variables in quantum theory. We argue that the appropriate quantum arena for an analysis of the properties of the Wick rotation is the diffeomorphism invariant Hilbert space of Loop Quantum Gravity (LQG) rather than its kinematic Hilbert space. We examine issues related to the construction, in quantum theory, of the positive complexifier as a positive operator on this diffeomorphism invariant Hilbert space. Assuming the existence of such an operator, we explore the possibility of identifying physical states in Lorentzian LQG as Wick rotated images of physical states in the Euclidean theory. Our considerations derive from Thiemann's remarkable proposal to define Lorentzian LQG from Euclidean LQG via the implementation in quantum theory of a phase space `Wick rotation' which maps real Ashtekar-Barbero variables to Ashtekar's complex, self dual variables.

https://arxiv.org/abs/1808.01252

**A review on Loop Quantum Gravity**

Pablo Antonio Moreno Casares

(Submitted on 3 Aug 2018)

The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for the theory: the canonical quantization (first two chapters) and spin foams (third). The final chapter will be devoted to studying some of the problems of the theory and what things remain to be developed. In chapter 3 we will also include an example of a simple calculation done in the frame of LQG: Schwarzschild black hole entropy.

https://arxiv.org/abs/1808.01744

**The no-boundary wave function for loop quantum cosmology**

Suddhasattwa Brahma, Dong-han Yeom

(Submitted on 6 Aug 2018)

Proposing smooth initial conditions is one of the most important tasks in quantum cosmology. On the other hand, the low-energy effective action, appearing in the semiclassical path integral, can get nontrivial quantum corrections near classical singularities due to specific quantum gravity proposals. In this article, we combine the well-known no-boundary proposal for the wavefunction of the universe with quantum modifications coming from loop quantum cosmology (LQC). Remarkably, we find that the restriction of a `slow-roll' type potential in the original Hartle-Hawking proposal is considerably relaxed due to quantum geometry regularizations. Interestingly, the same effects responsible for singularity-resolution in LQC also end up expanding the allowed space of smooth initial conditions leading to an inflationary universe.