Flat Potential for Inflaton with a Discrete $R$-invariance in Supergravity

Abstract

We show that a very flat potential of inflaton required for a sufficient inflation is naturally obtained in $N=1$ supergravity by imposing a discrete $R$-invariance $Z_{n}$. Several cosmological constraints on parameters in the inflaton superpotential are derived. The reheating temperature turns out to be $(1-10^8)$GeV for the cases of $n$=3--10. Baryogenesis in this model is also discussed briefly.