  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.
