Testing supersymmetric grand unified models of inflation

We reconsider a class of well motivated supersymmetric models in which inflation is associated with the breaking of a gauge symmetry G to H, with the symmetry breaking scale M∼1016 GeV. Starting with a renormalizable superpotential, we include both radiative and supergravity corrections to derive the inflationary potential. The scalar spectral index ns can exceed unity in some cases, and it cannot be smaller than 0.98 if the number of e-foldings corresponding to the present horizon scale is around 60. Two distinct variations of this scenario are discussed in which non-renormalizable terms allowed by the symmetries are included in the superpotential, and one finds ns≥0.97. The models discussed feature a tensor to scalar ratio r < or approx. 10-4, while dns/dlnk∼<10-3. If G corresponds to SO(10) or one of its rank five subgroups, the observed baryon asymmetry is naturally explained via leptogenesis