SELF-CONSISTENT SOLUTIONS OF THE SEMICLASSICAL EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

The general solution to the semiclassical backreaction equation is fou nd for conformally invariant free quantum fields in spatially flat hom ogeneous and isotropic spacetime with cosmological constant and with n o classical source when the ratio of the renormalisation parameters be ta/alpha = 9/4. It contains a two-parameter family of bouncing solutio ns that avoid the singularity. There are several one-parameter familie s which do not have particle horizons. The stability of these solution s is investigated and it is found that they are stable when alpha and lambda have different signs. However, when both parameters have the sa me sign the set of stable solutions is restricted by the condition 0 < lambda < 1/9. ln both cases these solutions have a final de Sitter st age.