  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
