Quantum Gowdy model within the new loop quantum cosmology improved dynamics

TL;DR

This paper presents a hybrid loop and Fock quantization of the Gowdy T^3 model, resolving singularities and establishing a well-defined evolution, thus advancing quantum cosmology models with inhomogeneities.

Contribution

It introduces a novel hybrid quantization scheme combining loop and Fock methods for the Gowdy T^3 model, demonstrating singularity resolution and consistent evolution.

Findings

Resolution of cosmological singularity

Construction of physical Hilbert space

Recovery of standard quantum field theory for inhomogeneities

Abstract

The linearly polarized Gowdy $T^3$ model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities.