Non-perturbative non-Gaussianity and primordial black holes

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