Gravitino thermal production revisited

TL;DR

This paper recalculates the gravitino production rate in the early universe, correcting previous errors and providing a new formula to estimate its abundance based on reheating temperature.

Contribution

It introduces a revised calculation of gravitino production, including previously overlooked processes, and offers a practical formula for cosmological applications.

Findings

Gravitino production rate is revised downward by nearly 10%.

New processes contributing to gravitino production are identified.

A convenient formula for gravitino abundance as a function of reheating temperature is provided.

Abstract

We calculate the gravitino production rate, computing its one-loop thermal self-energy. Gravitino production processes that do not result through thermal cuts of its self-energy, have been identified and taken into account. Correcting analytical errors and numerical approximations in the previous calculations, we present our result. This deviates from the latest estimation by almost 10%. More importantly, we provide a convenient formula, for calculating the gravitino production rate and its thermal abundance, as a function of the reheating temperature of the Universe.