Inflationary preheating and primordial black holes

Preheating after inflation may overproduce primordial black holes (PBH's) in many regions of parameter space. As an example we study two-field models with a massless self-interacting inflation, taking into account second order field and metric back reaction effects as spatial averages. We find that a complex quilt of parameter regions above the Gaussian PBH overproduction threshold emerges due to the enhancement of curvature perturbations on all scales. It should be possible to constrain realistic models of inflation through PBH overproduction although many issues, such as rescattering and non-Gaussianity, remain unsolved or unexplored.