Degenerate or Hierarchical Neutrinos in Supersymmetric Inflation

Two moderate extensions of the minimal supersymmetric standard model are considered. The first one includes a U(1)_{B-L} gauge group, while the second is based on a left-right symmetric gauge group. In these models, hybrid inflation is `naturally' realized and the mu problem is solved via a Peccei-Quinn symmetry. Baryon number conservation is an automatic consequence of a R-symmetry. The baryon asymmetry of the universe is generated through a primordial leptogenesis. In the `B-L' case, neutrinos are assumed to acquire degenerate masses equal to about 1.5 eV by coupling to SU(2)_L triplet superfields, thereby providing the hot dark matter of the universe. In the `left-right' model, light neutrinos acquire hierarchical masses by the seesaw mechanism. They are taken from the small angle MSW resolution of the solar neutrino puzzle and the SuperKamiokande data. Maximal nu_{mu}-nu_{tau} mixing, implied by the same data, is easily accommodated. The gravitino and baryogenesis constraints can be satisfied, in both models, with more or less `natural' values of the relevant coupling constants.