Volume modulus inflection point inflation and the gravitino mass problem

TL;DR

This paper explores inflection point inflation models with the volume modulus, analyzing how non-perturbative superpotentials and higher order corrections influence the gravitino mass, stability, and fine-tuning requirements.

Contribution

It investigates the impact of non-perturbative superpotentials and higher order corrections on volume modulus inflation, highlighting conditions for light gravitino and stability near the inflection point.

Findings

Light gravitino possible with positive exponent non-perturbative terms

Higher order corrections stabilize the axion direction

Time-dependent potentials address initial conditions only in heavy gravitino models

Abstract

Several models of inflection point inflation with the volume modulus as the inflaton are investigated. Non-perturbative superpotentials containing two gaugino condensation terms or one such term with threshold corrections are considered. It is shown that the gravitino mass may be much smaller than the Hubble scale during inflation if at least one of the non-perturbative terms has a positive exponent. Higher order corrections to the Kahler potential have to be taken into account in such models. Those corrections are used to stabilize the potential in the axion direction in the vicinity of the inflection point. Models with only negative exponents require uplifting and in consequence have the supersymmetry breaking scale higher than the inflation scale. Fine-tuning of parameters and initial conditions is analyzed in some detail for both types of models. It is found that fine-tuning of parameters in models with heavy gravitino is much stronger than in models with light gravitino. It is shown that recently proposed time dependent potentials can provide a solution to the problem of the initial conditions only in models with heavy gravitino. Such potentials can not be used to relax fine tuning of parameters in any model because this would lead to values of the spectral index well outside the experimental bounds.