Research on three major problems concerned with the early universe will be conducted: The first consists of solving the semiclassical backreaction equations when nonconformally coupled free scalar fields are present in homogeneous and isotropic spacetimes. Two aspects of this are of particular interest. One is the initial behaviors of the solutions, as that will determine whether they have initial singularities or particle horizons. The second is how Starobinsky's inflationary models and the R models of Mijic et. al. are affected by the presence of non-conformal fields during the inflationary phase. The second research project consists of solving the backreaction problem for free scalar fields in anisotropic spacetimes. It is of interest to see whether quantum effects change the nature of the singularities in these spacetimes. Also quantitative predictions for the amounts of anisotropy that can be dissipated in various models via particle production will be obtained. The third research project will be an investigation of spontaneous symmetry breaking in spacetimes with compact spatial sections for models with N scalar fields with quartic self- couplings. It has already been shown that spontaneous symmetry breaking for these models in the large N limit does not occur in the Einstein universe. If this result is more general, then it may be of great importance to cosmology.
