Quantum Cosmological Backreactions II: Purely Homogeneous Quantum Cosmology

TL;DR

This paper demonstrates how backreactions in quantum cosmology, studied through space adiabatic perturbation theory, introduce important correction terms in effective Hamiltonians, with implications for models like Loop Quantum Cosmology.

Contribution

It applies space adiabatic perturbation theory to simple models to show backreactions cause significant corrections in quantum cosmological effective Hamiltonians.

Findings

Backreactions lead to additional correction terms in effective Hamiltonians.

Toy models illustrate the formalism and effects of backreactions.

Results have potential implications for quantum cosmological theories like LQC.

Abstract

This is the second paper in a series of four in which we use space adiabatic methods in order to incorporate backreactions among the homogeneous and between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory. The purpose of the present paper is twofold. On the one hand, it illustrates the formalism of space adiabatic perturbation theory (SAPT) for two simple quantum mechanical toy models. On the other, it proves the main point, namely that backreactions lead to additional correction terms in effective Hamiltonians that one would otherwise neglect in a crude Born-Oppenheimer approximation. The first model that we consider is a harmonic oscillator coupled to an anharmonic oscillator. We chose it because it displays many similarities with the more interesting second model describing the coupling between an inflaton and gravity restricted to the purely homogeneous and isotropic sector. These results have potential phenomenological consequences in particular for quantum cosmological theories describing big bounces such as Loop Quantum Cosmology (LQC).