Kähler potentials for the minimally supersymmetric standard model inflation and thespectral index

Abstract

Recently it has been argued that some of the fine-tuning problems of the minimallysupersymmetric standard model (MSSM) inflation associated with the existence of a saddlepoint along a flat direction may be solved naturally in a class of supergravity models. Herewe extend the analysis and show that the constraints on the Kähler potentials in thesemodels are considerably relaxed when the location of the saddle point is treated as a freevariable. We also examine the effect of supergravity corrections on inflationarypredictions and find that they can slightly alter the value of the spectral index.As an example, for flat direction field values we find n∼0.92...0.94 while the prediction of the MSSM inflation without any corrections isn∼0.92.