Gravitino Problem in Inflation Driven by Inflaton-Polonyi K\"ahler Coupling

TL;DR

This paper examines the gravitino overproduction issue in inflation models with K"ahler potential-driven potentials, highlighting the decay channels leading to the problem and proposing potential solutions.

Contribution

It identifies the gravitino problem arising from inflaton decay in K"ahler potential-based inflation models and suggests ways to mitigate this issue.

Findings

Inflaton decays predominantly into inflatino and gravitino.

The gravitino problem is significant in models with inflaton-Polonyi coupling.

Proposed solutions could alleviate gravitino overproduction in these models.

Abstract

We discuss the cosmological gravitino problem in inflation models in which the inflaton potential is constructed from K\"ahler potential rather than superpotential: a representative model is $\overline{\text{D}3}$-induced geometric inflation. A critical ingredient in this type of models is the coupling of the inflaton and Polonyi (supersymmetry-breaking) field in the K\"ahler potential, which is needed to build the inflaton potential. We point out the same coupling let the inflaton dominantly decay into a pair of inflatino and gravitino causing the gravitino problem. We propose some possible solutions to this problem.