The well-known hybrid inflation has rich phenomena around its phase transition.
In some parameter regions, a long (mild) waterfall phase can be realized,
and in such a case, the generated curvature perturbations will be quite large because
the inflatons’ potential is flat around the critical point.
With a more than a few e-folds waterfall phase, therefore a peak feature will appear in
the power spectrum on relatively large scale comparing with the scale of the end of inflation,
and may cause massive primordial black holes (PBHs).
However, around the critical point, the standard linear perturbation theory for perturbations
is not available since quantum noise dominates over the classical potential force.
We have proposed a new algorithm with which the curvature perturbations can be calculated
non-perturbatively, by combining the stochastic inflation formalism and the deltaN formalism.
We have numerically calculated the PBH mass spectrum as well as the peaky power spectrum
around the critical point.