Local rotational symmetry Gowdy model in Loop Quantum Gravity

TL;DR

This paper presents a complete loop quantum gravity quantization of the Gowdy model with local rotational symmetry, resulting in a singularity-free quantum description and a novel discretization of spatial geometry.

Contribution

It introduces a new classical constraint algebra and constructs exact quantum solutions, physical Hilbert space, and observables for the model.

Findings

Singularity-free quantum spacetime emerges.

Exact solutions and physical Hilbert space constructed.

New quantum observable discretizes spatial geometry.

Abstract

We provide a complete quantization for the Gowdy model with local rotational symmetry in vacuum. We start with a redefinition of the classical constraint algebra such that the Hamiltonian constraint has a vanishing Poisson bracket with itself. We apply a canonical quantization within loop quantum gravity and an improved dynamics scheme. We construct the exact solutions to the constraints and the physical Hilbert space, together with the physical observables. The quantization provides a physical picture without singularities. Besides, a genuine discretization of the spatial geometry emerges by means of a new quantum observable without classical analogue.