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 (the spectral index n is approximately 0.98) with amplitude proportional to (M/M_{Planck})^2, where M ~ 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 approximately 2 x 10^{13} GeV and 6 x 10^9 GeV.