PBH in single field inflation: the effect of shape dispersion and
  non-Gaussianities
  Primordial black holes (PBHs) may result from high peaks in a random field of
cosmological perturbations. In single field inflationary models, such
perturbations can be seeded as the inflaton overshoots a small barrier on its
way down the potential. PBHs are then produced through two distinct mechanisms,
during the radiation era. The first one is the familiar collapse of large
adiabatic overdensities. The second one is the collapse induced by relic
bubbles where the inflaton field is trapped in a false vacuum, due to large
backward fluctuations which prevented horizon sized regions from overshooting
the barrier. We consider (numerically and analytically) the effect of
non-Gaussianities on the threshold for overdensities to collapse into a PBH.
Since typical high peaks have some dispersion in their shape or profile, we
also consider the effect of such dispersion on the corresponding threshold for
collapse. With these results we estimate the most likely channel for PBH
production as a function of the non-Gaussianity parameter $f_{\rm NL}$. We also
compare the threshold for collapse coming from the perturbative versus the non
perturbative template for the non-Gaussianity arising in this model. We show
that i) for $f_{\rm NL}\gtrsim 3.5$, the population of PBH coming from false
vacuum regions dominates over that which comes from the collapse of large
adiabatic overdensities, ii) the non-perturbative template of the
non-Gaussianities is important to get accurate results. iii) the effect of the
dispersion is small in determining the threshold for the compaction function,
although it can be appreciable in determining the threshold amplitude for the
curvature perturbation at low $f_{\rm NL}$. We also confirm that the volume
averaged compaction function provides a very accurate universal estimator for
the threshold.
