Post-Inflationary Gravitino Production Revisited

TL;DR

This paper reevaluates gravitino production after inflation, showing that thermal production dominates and providing updated estimates relevant for inflation models, especially in supersymmetric contexts.

Contribution

It demonstrates that gravitino production prior to complete reheating is negligible and confirms the standard thermal calculation as a good approximation.

Findings

Thermal gravitino production dominates over non-thermal contributions.

Instantaneous thermalization is a valid approximation in most scenarios.

Updated gravitino-to-entropy ratio estimates inform inflation model constraints.

Abstract

We revisit gravitino production following inflation. As a first step, we review the standard calculation of gravitino production in the thermal plasma formed at the end of post-inflationary reheating when the inflaton has completely decayed. Next we consider gravitino production prior to the completion of reheating, assuming that the inflaton decay products thermalize instantaneously while they are still dilute. We then argue that instantaneous thermalization is in general a good approximation, and also show that the contribution of non-thermal gravitino production via the collisions of inflaton decay products prior to thermalization is relatively small. Our final estimate of the gravitino-to-entropy ratio is approximated well by a standard calculation of gravitino production in the post-inflationary thermal plasma assuming total instantaneous decay and thermalization at a time $t \simeq 1.2/\Gamma_\phi$. Finally, in light of our calculations, we consider potential implications of upper limits on the gravitino abundance for models of inflation, with particular attention to scenarios for inflaton decays in supersymmetric Starobinsky-like models.