A simple extension of the minimal left-right symmetric supersymmetric grand
unified theory model is constructed by adding two pairs of superfields. This
naturally violates the partial Yukawa unification predicted by the minimal
model. After including supergravity corrections, we find that this extended
model naturally supports hilltop F-term hybrid inflation along its trivial
inflationary path with only a very mild tuning of the initial conditions. With
a convenient choice of signs of the terms in the Kahler potential, we can
reconcile the inflationary scale with the supersymmetric grand unified theory
scale. All the current data on the inflationary observables are readily
reproduced. Inflation is followed by non-thermal leptogenesis via the decay of
the right-handed neutrinos emerging from the decay of the inflaton and any
possible washout of the lepton asymmetry is avoided thanks to the violation of
partial Yukawa unification. The extra superfields also assist us in reducing
the reheat temperature so as to satisfy the gravitino constraint. The observed
baryon asymmetry of the universe is naturally reproduced consistently with the
neutrino oscillation parameters.Comment: 20 pages including 4 figure
