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