Leptogenesis in a Realistic Supersymmetric Model of Inflation with a Low Reheat Temperature

We discuss leptogenesis in a realistic supersymmetric model of inflation with a low reheat temperature 1-10 GeV. The lepton asymmetry is generated by a decaying right handed sneutrino, which is produced after inflation during preheating. The inflationary model is based on a simple variant of the Next-to-Minimal Supersymmetric Standard model (NMSSM) which solves the \mu problem, called \phiNMSSM, where the additional singlet \phi plays the role of the inflaton in hybrid (or inverted hybrid) type models. The model is invariant under an approximate Peccei-Quinn symmetry which also solves the strong CP problem, and leads to an invisible axion with interesting cosmological consequences. We show how the baryon number of the universe and the nature of cold dark matter are determined by the same parameters controlling the strong CP problem, the \mu problem and the neutrino masses and mixing angles