Volume modulus inflation and a low scale of SUSY breaking

Abstract

The relation between the Hubble constant and the scale of supersymmetry breaking isinvestigated in models of inflation dominated by a string modulus. Usually in this kind ofmodel the gravitino mass is of the same order of magnitude as the Hubble constant, whichis not desirable from the phenomenological point of view. It is shown that slow-roll saddlepoint inflation may be compatible with a low scale of supersymmetry breaking only if somecorrections to the lowest-order Kähler potential are taken into account. However,choosing an appropriate Kähler potential is not enough. There are also conditionsfor the superpotential and, for example, the popular racetrack superpotentialturns out to be not suitable. A model is proposed in which slow-roll inflation anda light gravitino are compatible. It is based on a superpotential with a triplegaugino condensation and the Kähler potential with the leading string corrections.The problem of fine-tuning and experimental constraints are discussed for thatmodel.