Backreaction and order reduction in initially contracting models of the universe
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.