Non-gaussianities for primordial black hole formation

TL;DR

This paper investigates how non-gaussianities during ultra-slow inflation phases affect primordial black hole formation, showing they significantly alter abundance estimates but can be balanced by slight parameter adjustments.

Contribution

It provides the first detailed calculation of non-gaussianities in ultra-slow inflation scenarios relevant for primordial black holes, and assesses their impact on abundance predictions.

Findings

Non-gaussianities are sizable and mainly local.

They significantly modify primordial black hole abundance estimates.

Small parameter tuning can compensate for non-gaussian effects.

Abstract

We analyze primordial non-gaussianities in presence of an ultra-slow phase during the inflationary dynamics, focusing on scenarios relevant for the production of primordial black holes. We compute the three-point correlation function of comoving curvature perturbations finding that non-gaussianities are sizable, and predominantly local. In the context of threshold statistics, we analyze their impact for the abundance of primordial black holes, and their interplay with the non-gaussianities arising from the non-linear relation between density and curvature perturbations. We find that non-gaussianities significantly modify the estimate of the primordial black holes abundance obtained with the gaussian approximation. However, we show that this effect can be compensated by a small change, of a factor $2\div3$ at most, of the amplitude of the primordial power spectrum of curvature perturbations. This is obtained with a small tuning of the parameters of the inflationary model.