  We show how hybrid inflation can be successfully realized in a supersymmetric
model with gauge group G_{PS}= SU(4)_c x SU(2)_L x SU(2)_R. By including a
non-renormalizable superpotential term, we generate an inflationary valley
along which G_{PS} is broken to the standard model gauge group. Thus,
catastrophic production of the doubly charged magnetic monopoles, which are
predicted by the model, cannot occur at the end of inflation. The results of
the cosmic background explorer can be reproduced with natural values (of order
10^{-3}) of the relevant coupling constant, and symmetry breaking scale of
G_{PS} close to 10^{16} GeV. The spectral index of density perturbations lies
between unity and 0.9. Moreover, the mu-term is generated via a Peccei-Quinn
symmetry and proton is practically stable. Baryogenesis in the universe takes
place via leptogenesis. The low deuterium abundance constraint on the baryon
asymmetry, the gravitino limit on the reheat temperature and the requirement of
almost maximal mu neutrino - tau neutrino mixing from SuperKamiokande can be
simultaneously met with mu-neutrino, tau-neutrino and heaviest Dirac neutrino
masses determined from the large angle MSW resolution of the solar neutrino
problem, the SuperKamiokande results and SU(4)_c symmetry respectively.
