Solving peak theory in the presence of local non-gaussianities

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 overestimates, 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.

Automated summary

The study investigates the probability density distribution of maxima for a scalar random field in the presence of local non-gaussianities. It finds that the impact of local non-gaussianities on the abundance of primordial black holes (PBHs) has been overestimated in previous literature by many orders of magnitude. By adjusting the peak amplitude of the curvature power spectrum, one can obtain the same abundance as predicted by the gaussian approximation in realistic single-field inflationary models with ultra slow-roll.