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

The general solution to the semiclassical back-reaction equations for conformally invariant quantum free fields is found in spatially flat h omogeneous and isotropic spacetimes containing an unquantized Dirac fi eld and cosmological constant when the ratio of the renormalization pa rameters beta/alpha is 9/4. It shows two-parameter families of bouncin g solutions which avoid the singularity. There are several one-paramet er families without particle horizons. The stability of the solutions which have a final de Sitter stage is investigated.