Supersymmetric inflation with constraints on superheavy neutrino masses

Abstract

We consider a supersymmetric model of inflation in which the primordial density fluctuations are nearly scale invariant (spectral index $n\ensuremath{\approx}0.98)$ with an amplitude proportional to ${(M/M}_{\mathrm{Planck}}{)}^{2}$, where $M\ensuremath{\sim}{10}^{16}$ 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 $\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{13}$ GeV and $6\ifmmode\times\else\texttimes\fi{}{10}^{9}$ GeV.