Natural Chaotic Inflation in Supergravity and Leptogenesis

We comprehensively investigate a chaotic inflation model proposed recently in the framework of supergravity. In this model, the form of K\"ahler potential is determined by a symmetry, that is, the Nambu-Goldstone like shift symmetry, which guarantees the absence of the exponential factor in the potential for the inflaton field. Though we need introduction of small parameters, the smallness of parameters is justified also by symmetries. That is, the zero limit of small parameters recovers symmetries, which is natural in 't Hooft's sense. The leptogenesis scenario via the inflaton decay in this chaotic inflation model is also discussed. We find that the lepton asymmetry enough to explain the present baryon number density is produced for low reheating temperatures avoiding the overproduction of gravitinos