Backreaction effects in initially contracting models of Universe with different order reduction methods applied*

The effects of particle production due to a quantized massive conformally coupled scalar field on the evolution of the Universe are considered for models in which there is a positive cosmological constant and the Universe initially is in a contracting de Sitter phase. Different adiabatic in states for the field are considered. The stress-energy tensor for the massive scalar field is renormalized using adiabatic regularization. This introduces higher derivative terms in the semiclassical backreaction equations which result in extra solutions that can often be physically unrealistic. Several methods similar to that of order reduction are used to eliminate these extra solutions and a comparison of the results is made.