The hybrid inflation waterfall and the primordial curvature perturbation
  Without demanding a specific form for the inflaton potential, we obtain an
estimate of the contribution to the curvature perturbation generated during the
linear era of the hybrid inflation waterfall. The spectrum of this contribution
peaks at some wavenumber $k=k_*$, and goes like $k^3$ for $k\ll k_*$, making it
typically negligible on cosmological scales. The scale $k_*$ can be outside the
horizon at the end of inflation, in which case $\zeta=- (g^2 - \vev{g^2})$ with
$g$ gaussian. Taking this into account, the cosmological bound on the abundance
of black holes is likely to be satisfied if the curvaton mass $m$ much bigger
than the Hubble parameter $H$, but is likely to be violated if $m\lsim H$.
Coming to the contribution to $\zeta$ from the rest of the waterfall, we are
led to consider the use of the `end-of-inflation' formula, giving the
contribution to $\zeta$ generated during a sufficiently sharp transition from
nearly-exponential inflation to non-inflation, and we state for the first time
the criterion for the transition to be sufficiently sharp. Our formulas are
applied to supersymmetric GUT inflation and to supernatural/running-mass
inflation
