The gravitino abundance in supersymmetric `new' inflation models

Abstract

We consider the abundance of gravitinos created from the vacuum fluctuation, in a class of `new' inflation models for which global supersymmetry is a good approximation. Immediately after inflation, gravitinos are produced, with number density determined by equations recently presented by Kallosh et. al. (hep-th/9907124) and Giudice et. al. (hep-ph/9907510). Unless reheating intervenes, creation may continue, maintaining about the same number density, until the Hubble parameter falls below the gravitino mass. In any case, the abundance of gravitinos created from the vacuum fluctuation exceeds the abundance from thermal collisions in a significant regime of parameter space, leading to tighter cosmological constraints.