Non-perturbative non-Gaussianity and primordial black holes

Abstract

We present a non-perturbative method for calculating the abundance of primordial 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 intermediate 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.

9 pages, 2 figures; Version 3: matches published version

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