Energy Spectra in Inflationary Models

Curvature effects in inflationary Robertson-Walker models, although neg ligible at the present day, can drastically alter the energy spectra of non-zero spin quantum fields in k ≠ 0 universes at early times. This affects the thermal energy densities of quantum fields, and hence the dynamical evolution of the universe. It is argued that, for k ≠ 0 universes with temperature T and spatial curvature R, if the inflation factor were so large that RT<~10^(-6+2k) before inflation, then there was never a pre-inflationary era in new inflation when the universe evolved according to the classical Einstein equations, but that the inflationary epoch must have grown directly out of the quantum gravity era