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 h similar to 1 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.