A complete hybrid quantization in inhomogeneous cosmology

TL;DR

This paper presents a comprehensive hybrid quantization approach for inhomogeneous cosmology within Loop Quantum Cosmology, combining background quantization with perturbative inhomogeneities, resulting in a unique Fock representation.

Contribution

It introduces a complete hybrid quantization scheme for inhomogeneous cosmology, integrating LQC background quantization with a Fock quantization of inhomogeneities, ensuring uniqueness and invariance.

Findings

Unique Fock representation identified for inhomogeneities

Hybrid quantization successfully incorporates inhomogeneities into LQC

Framework maintains invariance under spatial isometries and unitarity

Abstract

A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case of compact spatial topology, the requirements of: i) invariance under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a unique Fock representation and a particular set of canonical fields (up to unitary equivalence).