Primordial black hole abundance: The importance of broadness

Abstract

We show that the abundance of primordial black holes, if formed through the collapse of large fluctuations generated during inflation and unless the power spectrum of the curvature perturbation is very peaked, is always dominated by the broadest profile of the compaction function, where the corresponding threshold is $2/5$, even though statistically it is not the most frequent. This result exacerbates the tension when combining the primordial black hole abundance with the signal seen by pulsar timing arrays and originated from gravitational waves induced by the same large primordial perturbations.