Solving peak theory in the presence of local non-gaussianities

TL;DR

This paper calculates the probability distribution of maxima in a scalar field with local non-gaussianities, showing that their impact on primordial black hole abundance is much smaller than previously thought, especially in single-field inflation models.

Contribution

It provides a corrected analysis of non-gaussianities' effect on PBH formation, demonstrating minimal impact in realistic inflationary scenarios.

Findings

Non-gaussianities have a negligible effect on PBH abundance in realistic models.

Previous estimates significantly overstate the impact of non-gaussianities.

The required change in the curvature power spectrum amplitude is at most a factor of two.

Abstract

We compute the probability density distribution of maxima for a scalar random field in the presence of local non-gaussianities. The physics outcome of this analysis is the following. If we focus on maxima whose curvature is larger than a certain threshold for gravitational collapse, our calculations illustrate how the fraction of the Universe's mass in the form of primordial black holes (PBHs) changes in the presence of local non-gaussianities. We find that previous literature on the subject exponentially overestimate, by many orders of magnitude, the impact of local non-gaussianities on the PBH abundance. We explain the origin of this discrepancy, and conclude that, in realistic single-field inflationary models with ultra slow-roll, one can obtain the same abundance found with the gaussian approximation simply changing the peak amplitude of the curvature power spectrum by no more than a factor of two. We comment about the relevance of non-gaussianities for second-order gravitational waves.