Abstract
Some properties of the particle-creation rate by an interaction in two expanding model-universes with a big-bang origin are investigated by using a perturbative S-matrix formalism. It is shown that, in most cases, the lowest order particle creation rate from vacuum diverge in ultra-violet and infra-red regions in the summation of phase space. This is a new type of divergences owing to the expansion of the universe. We must then conclude that the perturbative S-matrix formulation is not in general available in a curved spacetime.

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