A Next-to-Minimal model of Hybrid Inflation in Effective Supergravity Theories

We propose a model of inflation based on a simple variant of the NMSSM, called $\phi$NMSSM where the additional singlet $\phi$ plays the role of the inflaton in hybrid (or inverted hybrid) type models. The $\phi$NMSSM solves the $\mu$ problem of the MSSM via the vacuum expectation value of the gauge singlet N, but also solves the strong CP problem through an approximate Peccei-Quinn symmetry. The potential energy which drives inflation originates from the F-term of the effective supergravity theory which result from a generic string theory. In the class of models considered the inflaton is protected from receiving mass during inflation by a Heisenberg symmetry, avoiding the $\eta$ problem.