Volume modulus inflection point inflation and the gravitino mass problem

Abstract

Several models of inflection point inflation with the volumemodulus as the inflaton are investigated. Non-perturbativesuperpotentials containing two gaugino condensation terms orone such term with threshold corrections are considered.It is shown that the gravitino mass may be much smaller thanthe Hubble scale during inflation if at least one of thenon-perturbative terms has a positive exponent.Higher order corrections to the Kähler potential have to betaken into account in such models.Those corrections are used to stabilize the potential inthe axion direction in the vicinity of the inflection point.Models with only negative exponents require uplifting andin consequence have the supersymmetry breaking scale higherthan the inflation scale. Fine-tuning of parameters and initialconditions is analyzed in some detail for both types of models.It is found that fine-tuning of parametersin models with heavy gravitino is much stronger than in modelswith light gravitino.It is shown that recently proposed time dependent potentialscan provide a solution to the problem of the initial conditionsonly in models with heavy gravitino. Such potentials can not beused to relax fine tuning of parameters in any model becausethis would lead to values of the spectral index well outsidethe experimental bounds.