  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.
