Hybrid quantization of an inflationary universe

TL;DR

This paper develops a complete loop quantum cosmology model of an inflationary universe with small inhomogeneities, combining polymeric and Fock quantizations to describe the quantum dynamics and physical states.

Contribution

It provides a novel hybrid quantization approach for an inflationary universe with inhomogeneities, unifying gauge-fixed and gauge-invariant descriptions at the quantum level.

Findings

Complete quantum description of an inflationary universe with inhomogeneities.

Construction of the physical Hilbert space and quantum Hamiltonian constraint.

Demonstration of unitary equivalence between different quantum descriptions.

Abstract

We quantize to completion an inflationary universe with small inhomogeneities in the framework of loop quantum cosmology. The homogeneous setting consists of a massive scalar field propagating in a closed, homogeneous scenario. We provide a complete quantum description of the system employing loop quantization techniques. After introducing small inhomogeneities as scalar perturbations, we identify the true physical degrees of freedom by means of a partial gauge fixing, removing all the local degrees of freedom except the matter perturbations. We finally combine a Fock description for the inhomogeneities with the polymeric quantization of the homogeneous background, providing the quantum Hamiltonian constraint of the composed system. Its solutions are then completely characterized, owing to the suitable choice of quantum constraint, and the physical Hilbert space is constructed. Finally, we consider the analog description for an alternate gauge and, moreover, in terms of gauge-invariant quantities. In the deparametrized model, all these descriptions are unitarily equivalent at the quantum level.