Nonlinear metric perturbations and production of primordial black holes

We consider a simple inflationary model with a peculiarity in the form of a ``plateau'' in the inflaton potential. We use the formalism of a coarse-grained field in order to describe the production of metric perturbations h of an arbitrary amplitude, and obtain a non-Gaussian probability function for such metric perturbations. We associate the spatial regions having large perturbations h1 with the regions going to primordial black holes after inflation. We show that in our model the nonlinear effects can lead to overproduction of primordial black holes.