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The dark matter in the universe can be in the form of a superheavy matter species (wimpzilla). Several mechanisms have been proposed for the production of wimpzilla particles during or immediately following the inflationary epoch. Perhaps the most attractive mechanism is through gravitational particle production, where particles are produced simply as a result of the expansion of the universe. In this paper we present a detailed numerical calculation of wimpzilla gravitational production in hybrid-inflation models and natural-inflation models. Generalizing these findings, we also explore the dependence of the gravitational production mechanism on various models of inflation. We show that superheavy dark matter production seems to be robust, with ₗh^2 (Mₗ/10^11GeV) ^2 (Tₑ₇/10^9GeV), so long as Mₗ<H₈, where Mₗ is the wimpzilla mass, Tₑ₇ is the reheat temperature, and H₈ is the expansion rate of the universe during inflation.
Chung et al. (Thu,) studied this question.