Abstract
A perturbative evaluation of the $S$ matrix is used to compute the production of particles in an expanding flat Friedmann-Robertson-Walker universe in the presence of small inhomogeneities. We first consider the production of massless conformally coupled and weakly nonconformally coupled particles, obtaining known results, and then we consider the production of massive particles. The production of massive particles cannot be treated only perturbatively and a method is proposed to compute this in general. The pair-production probability is computed using two different, but related, methods: in one we directly evaluate the number of particles produced and in the other we concentrate mainly on the vacuum-to-vacuum or vacuum persistence amplitude.
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