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Primordial black holes (PBHs) may result from high peaks in a random field ofcosmological perturbations. In single field inflationary models, suchperturbations can be seeded as the inflaton overshoots a small barrier on itsway down the potential. PBHs are then produced through two distinct mechanisms,during the radiation era. The first one is the familiar collapse of largeadiabatic overdensities. The second one is the collapse induced by relicbubbles where the inflaton field is trapped in a false vacuum, due to largebackward fluctuations which prevented horizon sized regions from overshootingthe barrier. We consider (numerically and analytically) the effect ofnon-Gaussianities on the threshold for overdensities to collapse into a PBH.Since typical high peaks have some dispersion in their shape or profile, wealso consider the effect of such dispersion on the corresponding threshold forcollapse. With these results we estimate the most likely channel for PBHproduction as a function of the non-Gaussianity parameter $f_{\rm NL}$. We alsocompare the threshold for collapse coming from the perturbative versus the nonperturbative template for the non-Gaussianity arising in this model. We showthat i) for $f_{\rm NL}\gtrsim 3.5$, the population of PBH coming from falsevacuum regions dominates over that which comes from the collapse of largeadiabatic overdensities, ii) the non-perturbative template of thenon-Gaussianities is important to get accurate results. iii) the effect of thedispersion is small in determining the threshold for the compaction function,although it can be appreciable in determining the threshold amplitude for thecurvature perturbation at low $f_{\rm NL}$. We also confirm that the volumeaveraged compaction function provides a very accurate universal estimator forthe threshold.

PBH in single field inflation: the effect of shape dispersion and non-Gaussianities