SELF-CONSISTENT SOLUTIONS OF THE SEMICLASSICAL BACK-REACTION EQUATIONS WITH COSMOLOGICAL CONSTANT SPATIAL CURVATURE AND PERFECT FLUID

Exact solutions of the semi-classical Einstein equations with cosmolog ical constant for conformally invariant free quantum fields in a gener al Robertson-Walker metric are found when a classical perfect fluid is present. There exist a one-parameter family of time-symmetric bouncin g solutions that avoid the singularity and a one-parameter family whic h does not have particles horizons. The de Sitter solution is found to be stable, while the Einstein universe is unstable.