Slow Roll during the Waterfall Regime: The Small Coupling Window for
  SUSY Hybrid Inflation
  It has recently been pointed out that a substantial amount of e-folds can
occur during the waterfall regime of hybrid inflation. Moreover, Kodama et.al.
have derived analytic approximations for the trajectories of the inflaton and
of the waterfall fields. Based on these, we derive here the consequences for F-
and D-term SUSY hybrid inflation: A substantial amount of e-folds may occur in
the waterfall regime, provided kappa << M^2/M_P^2, where kappa is the
superpotential coupling, M the scale of symmetry breaking and M_P the reduced
Planck mass. When this condition is amply fulfilled, a number of e-folds much
larger than N_e\approx60 can occur in the waterfall regime and the scalar
spectral index is then given by the expression found by Kodama et.al.
n_s=1-4/N_e. This value may be increased up to unity, if only about N_e e-folds
occur during the waterfall regime, such that the largest observable scale
leaves the horizon close to the critical point of hybrid inflation, what can be
achieved for kappa\approx10^(-13) and M\approx5x10^(12) GeV in F-term
inflation. Imposing the normalization of the power spectrum leads to a lower
bound on the scale of symmetry breaking.
