Supersymmetric Inflation at the Grand Unification Scale

We consider a supersymmetric model of inflation in which the primordial density fluctuations are nearly scale invariant (spectral index $n \approx 0.98$) with amplitude proportional to $(M/M_{P})^2$, where $M\sim 10^{16}$ GeV denotes the scale of the gauge symmetry breaking associated with inflation. The (roughly) 60 e-foldings take place when all relevant scales are close to $M$, so supergravity corrections are suppressed. The baryon asymmetry arises via leptogenesis and the dark matter is a mixture of `cold' (LSP) and `hot' ($\nu_\tau$) components which provides a consistent picture for the formation of large scale structure. Such models find a natural setting within supersymmetric ${\rm SO(10)}$ or ${\rm SU(3)_c \times SU(3)_L \times SU(3)_R}$.