Non-perturbative non-Gaussianity and primordial black holes

We present a non-perturbative method for calculating the abundance of primor-dial black holes given an arbitrary one-point probability distribution function for the primordial curvature perturbation, P(zeta). A non-perturbative method is essential when considering non-Gaussianities that cannot be treated using a conventional perturbative expansion. To determine the full statistics of the density field, we relate zeta to a Gaussian field by equating the cumulative distribution functions. We consider two examples: a specific local-type non-Gaussian distribution arising from ultra slow roll models, and a general piecewise model for P(zeta) with an exponential tail. We demonstrate that the enhancement of primordial black hole formation is due to the inter-mediate regime, rather than the far tail. We also show that non-Gaussianity can have a significant impact on the shape of the primordial black hole mass distribution.