Axion Inflation, Proton Decay and Leptogenesis in $SU(5)\times
  U(1)_{PQ}$
  We implement inflation in a non-supersymmetric SU(5) model based on a
non-minimal coupling of the axion field to gravity. The isocurvature
fluctuations are adequately suppressed, axions comprise the dark matter, proton
lifetime estimates are of order 8e34-3e35 years, and the observed baryon
asymmetry arises via non-thermal leptogenesis. The presence of low scale
colored scalars ensures unification of the Standard Model gauge couplings and
also helps in stabilizing the electroweak vacuum.
