Supersymmetric inflation with constraints on superheavy neutrino masses

We consider a supersymmetric model of inflation in which the primordial density fluctuations are nearly scale invariant (spectral index $n\approx 0.98)$ with an amplitude proportional to ${(M/M}_{\mathrm{Planck}}{)}^2$, where $M\sim {10}^{16}$ GeV denotes the scale of the gauge symmetry breaking associated with inflation. The 60 or so $e$ foldings take place when all relevant scales are close to $M$, which helps suppress supergravity corrections. The gravitino and baryogenesis (via leptogenesis) constraints help determine the two heaviest right-handed neutrino masses to be $\approx 2\times {10}^{13}$ GeV and $6\times {10}^9$ GeV.