Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model

TL;DR

This paper develops a hybrid quantum model for Gowdy spacetimes with inhomogeneities, combining loop and Fock quantizations, and compares two schemes within Loop Quantum Cosmology to address singularity resolution and quantum structure.

Contribution

It introduces and compares two hybrid quantization schemes for Gowdy models, advancing the understanding of inhomogeneous Loop Quantum Cosmology.

Findings

Quantum resolution of cosmological singularity.

Distinct superselection sectors identified.

Constructed Hilbert space of physical states.

Abstract

The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two different schemes for the quantization of the Bianchi I model within the {\sl improved dynamics} formalism of Loop Quantum Cosmology. One of these schemes has been recently put forward by Ashtekar and Wilson-Ewing. We address several issues including the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, or the construction of the Hilbert space of physical states.