Exact solutions of the Einstein equations including quantum effects and classical matter

The general solution to the semiclassical backreaction equations is found for conformally invariant free quantum fields in spatially flat homogeneous and isotropic spacetimes containing classical matter and no cosmological constant when the ratio of the renormalization parameters Β/α is 9/4. For both signs of α, there is always a matterdominated Friedmann solution and it is stable when α<0. If α>0, there are two two-parameter and four one-parameter families of time-non-symmetric bouncing solutions which contain no singularities and two of the latter have a final matter Friedmann stage. There are four one-parameter and four zero-parameter families of solutions with singularities and no particle horizons and two of the latter have a final matter Friedmann stage. The final behaviour of the solutions is investigated for other values of Β/α and the asymptotically de Sitter solutions are found to be stable when α>0. (author)