Non-perturbative non-Gaussianity and primordial black holes

Understand

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.