Thermal spectra in the early Universe

It is shown that curvature effects, though completely negligible at the present day, can drastically alter thermal spectra at early times in some inflationary cosmological models. This can lead to a modification of the thermal history of the universe before the entropy production. The effects are only present for spatially curved k not=0 Robertson-Walker models, not for spatially flat k=0 models. If the entropy increase is >> 1087 and k not=0 then the energy density in the quantum fields is much greater, and hence the universe is much younger, at the onset of inflation than would be the case in a spatially flat universe. The effect is not relevant for chaotic inflation