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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.