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The semiclassical backreaction equations are solved in closedRobertson-Walker spacetimes containing a positive cosmological constant and aconformally coupled massive scalar field. Renormalization of the stress-energytensor results in higher derivative terms that can lead to solutions that varyon much shorter time scales than the solutions that would occur if the higherderivative terms were not present. These extra solutions can be eliminatedthrough the use of order reduction. Four different methods of order reductionare investigated. These are first applied to the case when only conformallyinvariant fields, with and without classical radiation, are present. Then theyare applied to the massive conformally coupled scalar field. The effects ofdifferent adiabatic vacuum states for the massive field are considered. It isfound that if enough particles are produced, then the Universe collapses to afinal singularity. Otherwise it undergoes a bounce, but at a smaller value ofthe scale factor (for the models considered) than occurs for the classical deSitter solution. The stress-energy tensor incorporates both particle productionand vacuum polarization effects. An analysis of the energy density of themassive field is done to determine when the contribution from the particlesdominates.

Backreaction and order reduction in initially contracting models of the universe