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

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 $\hat{I}\P$ and the compaction $C$, finding that, whilst PBHs may form at rare peaks in $C$ these do not necessarily correspond to rare peaks in $\hat{I}\P$ - casting some doubt on many of the existing calculations of the PBH abundance.

18 pages, 3 figures (plus appendices: 4 pages, 2 figures). V2 and V3: updated to match published version, minor changes and corrections