Non-Minimal Higgs Inflation and non-Thermal Leptogenesis in a
  Supersymmetric Pati-Salam Model
  We consider a supersymmetric (SUSY) Grand Unified Theory (GUT) based on the
gauge group G_PS=SU(4)_C x SU(2)_L x SU(2)_R, which incorporates non-minimal
chaotic inflation, driven by a quartic potential associated with the Higgs
fields involved in the spontaneous breaking of G_PS. The inflationary model
relies on renormalizable superpotetial terms and does not lead to
overproduction of magnetic monopoles. It is largely independent of the one-loop
radiative corrections and can become consistent with the current observational
data on the inflationary observables, with the symmetry breaking scale of G_PS
assuming its SUSY value. Within our model, the strong CP and the mu problems of
the minimal supersymmetric standard model can be resolved via a Peccei-Quinn
symmetry. Moreover baryogenesis occurs via non-thermal leptogenesis realized by
the out-of-equilibrium decay of the right-handed neutrinos, which are produced
by the inflaton's decay. We consider two versions of such a scenario, assuming
that the inflaton can decay to the lightest or to the next-to-lightest
right-handed neutrino. Both scenaria can become compatible with the constraints
arising from the baryon asymmetry of the universe, the gravitino limit on the
reheating temperature and the upper bound on the light neutrino masses,
provided that the gravitino is somehow heavy. In the second scenario extra
restrictions from the SU(4)_C symmetry on the heaviest Dirac neutrino mass and
the data on the atmospheric neutrino oscillations can be also met.
