The gravitino abundance in supersymmetric `newʹ inflation models

We consider the abundance of gravitinos created from the vacuum fluctuation, in a class of `newʹ 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.