The Primordial Black Hole Abundance: The Broader, the Better

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, even though statistically it is not the most frequent. The corresponding threshold is therefore 2/5. 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.

V2, Published version on PRD. Minor changes respect V1

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• Induced Gravitational Waves probing Primordial Black Hole Dark Matter with Memory Burden
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• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
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• Is the formation of primordial black holes from single-field inflation compatible with standard cosmology?
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• Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer
• Beware of the running $n_s$ when producing heavy primordial black holes
• Excursion-set for Primordial Black Holes I: white noise and moving barrier
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• The Dark Side of the Moon: Listening to Scalar-Induced Gravitational Waves