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