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

Abstract

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