We identify a new inflationary regime for which more than 60 e-folds are
generated classically during the waterfall phase occuring after the usual
hybrid inflation. By performing a bayesian Monte-Carlo-Markov-Chain analysis,
this scenario is shown to take place in a large part of the parameter space of
the model. When this occurs, the observable perturbation modes leave the Hubble
radius during waterfall inflation. The power spectrum of adiabatic
perturbations is red, possibly in agreement with CMB constraints. A particular
attention has been given to study only the regions for which quantum
backreactions do not affect the classical dynamics. Implications concerning the
preheating and the absence of topological defects in our universe are
discussed.Comment: 10 pages, 5 figures, section III-A on quantum backreactions more
detailed, comments on transverse field gradient contribution added, version
accepted for publication in Phys.Rev.
