F-term Hybrid Inflation, the η-problem and Extra Dimensions

F-term hybrid inflation models in the context of supergravity generically have corrections to the inflaton mass squared of the order of H² (the η-problem). In addition they have a problem with large deviations of the spectrum of density perturbations from scale-invariance due to non-renormalizable corrections to the superpotential. Here we show that an increase of the expansion rate at large energy densities relative to that in conventional d = 4 cosmology, as suggested by brane scenarios, can naturally solve the η problem. For the case of a ρ² squared correction to H² suppressed by the brane tension this requires that the d = 5 Planck mass satisfies M₅≲10¹⁶ GeV. In addition, the scale-invariance of the density perturbation spectrum can be generally protected from Planck-suppressed superpotential corrections if M₅≲10¹⁰{ GeV}. Therefore brane cosmologies which produce an enhanced expansion rate at large energy densities are favoured by SUSY hybrid inflation.