Back Reaction and Semiclassical Approximation of cosmological models coupled to matter

TL;DR

This paper investigates the semiclassical quantum gravity of cosmological models coupled to matter, analyzing back reaction effects using different methods and highlighting discrepancies between them.

Contribution

It compares two approaches to calculate back reaction in semiclassical cosmology, revealing differences in their outcomes.

Findings

Different results obtained from Wigner function and energy-momentum tensor methods

Analysis of back reaction effects in Bianchi and FRW models

Insights into semiclassical approximation limitations

Abstract

Bianchi -I, -III, and FRW type models minimally coupled to a massive spatially homogeneous scalar field (i.e. a particle) are studied in the framework of semiclassical quantum gravity. In a first step we discuss the solutions of the corresponding equation for a Schr\"odinger particle propagating on a classical background. The back reaction of the Schr\"odinger particle on the classical metric is calculated by means of the Wigner function and by means of the expectation value of the energy-momentum-tensor of the field as a source. Both methods in general lead to different results.