Backreaction and order reduction in initially contracting models of the universe

TL;DR

This paper investigates the backreaction effects in contracting universe models with a cosmological constant and a scalar field, focusing on order reduction methods to eliminate unphysical solutions and analyzing conditions leading to collapse or bounce.

Contribution

It introduces and compares four order reduction techniques in semiclassical backreaction equations for contracting universe models with a scalar field.

Findings

Universe collapses to a singularity if enough particles are produced.

The universe undergoes a bounce at a smaller scale factor than classical de Sitter.

Particle production and vacuum polarization significantly influence the universe's evolution.

Abstract

The semiclassical backreaction equations are solved in closed Robertson-Walker spacetimes containing a positive cosmological constant and a conformally coupled massive scalar field. Renormalization of the stress-energy tensor results in higher derivative terms that can lead to solutions that vary on much shorter time scales than the solutions that would occur if the higher derivative terms were not present. These extra solutions can be eliminated through the use of order reduction. Four different methods of order reduction are investigated. These are first applied to the case when only conformally invariant fields, with and without classical radiation, are present. Then they are applied to the massive conformally coupled scalar field. The effects of different adiabatic vacuum states for the massive field are considered. It is found that if enough particles are produced, then the Universe collapses to a final singularity. Otherwise it undergoes a bounce, but at a smaller value of the scale factor (for the models considered) than occurs for the classical de Sitter solution. The stress-energy tensor incorporates both particle production and vacuum polarization effects. An analysis of the energy density of the massive field is done to determine when the contribution from the particles dominates.