Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations

TL;DR

This paper develops a hybrid quantization approach combining loop and Fock methods for inhomogeneous cosmological models, successfully resolving singularities and providing a robust framework for loop quantum cosmology with inhomogeneities.

Contribution

It introduces a novel hybrid quantization method that unifies loop and Fock techniques, effectively resolving singularities without special boundary conditions.

Findings

Singularity resolution achieved without boundary conditions

Operators for constraints are well-defined and consistent

Physical Hilbert space reproduces Fock quantization for inhomogeneities

Abstract

We quantize an inhomogeneous cosmological model using techniques that include polymeric quantization. More explicitly, we construct well defined operators to represent the constraints and find the physical Hilbert space formed by their solutions, which reproduces the conventional Fock quantization for the inhomogeneities. The initial singularity is resolved in this inhomogeneous model in an extremely simple way and without imposing special boundary conditions, thus ensuring the robustness and generality of this resolution. Furthermore this quantization constitutes a well founded step towards the extraction of physical results and consequences from loop quantum cosmology, given the central role of the inhomogeneities in modern cosmology.