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. The latter are due to rare backward fluctuations of the inflaton which prevented it from overshooting the barrier in horizon sized regions. 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_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_NL ≳ 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_NL. We also confirm that the volume averaged compaction function provides a very accurate universal estimator for the threshold.