Effects of quantum fields on singularities and particle horizons in the early universe

The back-reaction problem for conformally invariant free quantum fields in spatially flat homogeneous and isotropic spacetimes containing classical radiation is solved. The solutions depend upon two regularization parameters which we call and. Only solutions which at late times approach the appropriate solution to the field equations of general relativity are considered. For all and with >0 there are many such solutions, while for all and with 3>0, there is always one solution which undergoes a "time-symmetric bounce" and which contains no singularities or particle horizons. For >0 there is always at least one solution which begins with an initial singularity and which has no particle horizons. For all and there is always at least one solution which begins with an initial singularity.