Peaks and primordial black holes: the effect of non-Gaussianity

TL;DR

This paper re-evaluates the impact of local non-Gaussianity on primordial black hole abundance using peaks theory, finding the effects are less significant than previously thought and that constraints on non-Gaussianity are weaker.

Contribution

It applies peaks theory to the full non-linear compaction, providing a more accurate assessment of non-Gaussianity effects on PBH formation and constraints.

Findings

Non-Gaussianity effects are less significant than prior estimates.

Larger non-Gaussianity parameters are needed to match previous effects.

Correlation analysis questions the link between rare peaks in curvature and compaction.

Abstract

In light of recent developments in the field, we re-evaluate the effect of local-type non-Gaussianity on the primordial black hole (PBH) abundance (and consequently, upon constraints on the primordial power spectrum arising from PBHs). We apply peaks theory to the full, non-linear compaction, finding that, whilst the effect of non-Gaussianity is qualitatively similar to previous findings, the effect is much less significant. It is found the non-Gaussianity parameters $f_\mathrm{NL}^\mathrm{local}$ and $g_\mathrm{NL}^\mathrm{local}$ typically need to be approximately 1 or 2 orders of magntiude larger respectively to have a similar to that previously found. The effect will be to weaken the dependance of PBH constraints on the primordial power spectrum on the non-Gaussianity parameters, as well as to dramatically weaken constraints on the non-Gaussianity parameters (and/or PBH abundance) arising from the non-observation of dark matter isocurvature modes. We also consider the correlation between the curvature perturbation $\zeta$ and the compaction $C$, finding that, whilst PBHs may form at rare peaks in $C$ these do not necessarily correspond to rare peaks in $\zeta$ - casting some doubt on many of the existing calculations of the PBH abundance.