The Isaacson expansion in quantum cosmology

TL;DR

This paper applies the Isaacson and Born-Oppenheimer approximations to quantum cosmology, clarifying the role of semiclassical methods and backreaction in a perturbed minisuperspace model, and constructs both semiclassical and non-semiclassical solutions.

Contribution

It introduces a novel application of classical gravity and molecular physics approximations to quantum cosmology, providing new insights into semiclassical and quantum perturbation solutions.

Findings

Constructed non-semiclassical approximate solutions.

Developed semiclassical solutions with highly excited quantum perturbations.

Clarified the role of backreaction in the semiclassical approximation.

Abstract

This paper is an application of the ideas of the Born-Oppenheimer (or slow/fast) approximation in molecular physics and of the Isaacson (or short-wave) approximation in classical gravity to the canonical quantization of a perturbed minisuperspace model of the kind examined by Halliwell and Hawking. Its aim is the clarification of the role of the semiclassical approximation and the backreaction in such a model. Approximate solutions of the quantum model are constructed which are not semiclassical, and semiclassical solutions in which the quantum perturbations are highly excited.