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 $\alpha$ and $\beta$. Only solutions which at late times approach the appropriate solution to the field equations of general relativity are considered. For all $\alpha$ and $\beta$ with $\alpha >0\mathrm{}$ there are many such solutions, while for all $\alpha$ and $\beta$ with $\alpha <0\mathrm{}$ there is only one such solution. For $\beta >3\mathrm{}\alpha >0\mathrm{}$, there is always one solution which undergoes a "time-symmetric bounce" and which contains no singularities or particle horizons. For $\alpha >0\mathrm{}$ there is always at least one solution which begins with an initial singularity and which has no particle horizons. For all $\alpha$ and $\beta$ there is always at least one solution which begins with an initial singularity.