Effects of quantum fields on singularities and particle horizons in the early universe. IV. Initially empty universes

The behaviors of solutions to the semiclassical back-reaction equations are investigated for conformally invariant free quantum fields and a conformally coupled massive scalar field in spatially flat homogeneous and isotropic spacetimes with no classical radiation or matter. The quantum fields are all initially in their vacuum states. Only solutions beginning with the scale factor equal to zero are considered. The behaviors of solutions depend upon two regularization parameters {α} and {β} and on the mass m of the scalar field. For {β}{≥}3{α}>0, all solutions beginning with the scale factor equal to zero are without particle horizons, while for 3{α}>{β}>0 a one-parameter family of solutions with no particle horizons exists. For {β}>0, {α}<0 a one-parameter family of solutions with no singularities or particle horizons exists if m=0 and may exist if m{≠}0 as well. For m{≠}0, {α}>0 there is evidence that a one-parameter family of solutions which expand like classical matter-dominated Friedmann universes at late times compared to the Planck time exists. For {α}<0 a two-parameter family of such solutions exists. In both cases particle production due to the massive scalar field fills up the spacetimes.