Lp. Chimento et Na. Zuccala, SELF-CONSISTENT SOLUTIONS OF THE SEMICLASSICAL BACK-REACTION EQUATIONS WITH COSMOLOGICAL CONSTANT SPATIAL CURVATURE AND PERFECT FLUID, Astrophysics and space science, 215(2), 1994, pp. 229-236
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.