F-Term Hybrid Inflation, the \eta-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 H^{2} (the \eta-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 the single brane Randall-Sundrum scenario with an uncompactified extra dimension, can naturally solve the \eta problem. This requires that the d=5 Planck mass satisfies M_{5} < 10^{16} GeV. In addition, the scale-invariance of the density perturbation spectrum can be generally protected from Planck-suppressed superpotential corrections if M_{5} < 10^{10} \GeV