Hybrid Loop Quantum Cosmology: An Overview

TL;DR

This paper reviews the hybrid approach in Loop Quantum Cosmology, combining background quantum geometry with field quantization to study cosmological models and their potential observational consequences.

Contribution

It provides the first comprehensive review of the hybrid quantization approach applied to various cosmological spacetimes and perturbations.

Findings

Application to Gowdy spacetimes with gravitational waves

Analysis of cosmological perturbations during inflation

Potential for confronting quantum geometry effects with observations

Abstract

Loop Quantum Gravity is a nonperturbative and background independent program for the quantization of General Relativity. Its underlying formalism has been applied successfully to the study of cosmological spacetimes, both to test the principles and techniques of the theory and to discuss its physical consequences. These applications have opened a new area of research known as Loop Quantum Cosmology. The hybrid approach addresses the quantization of cosmological systems that include fields. This proposal combines the description of a finite number of degrees of freedom using Loop Quantum Cosmology, typically corresponding to a homogeneous background, and a Fock quantization of the field content of the model. In this review we first present a summary of the foundations of homogeneous Loop Quantum Cosmology and we then revisit the hybrid quantization approach, applying it to the study of Gowdy spacetimes with linearly polarized gravitational waves on toroidal spatial sections, and to the analysis of cosmological perturbations in preinflationary and inflationary stages of the Universe. The main challenge is to extract predictions about quantum geometry effects that eventually might be confronted with cosmological observations. This is the first extensive review of the hybrid approach in the literature on Loop Quantum Cosmology.