An accurate model for the primordial black hole mass distribution from a peak in the power spectrum

Understand

We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum.

• In light of improvements to the modelling, we revisit the claim that the effects of critical collapse produce a distribution that is not described by the commonly assumed lognormal, showing that this conclusion remains valid, particularly for narrow peaks where the shape of the mass distribution is insensitive to the peak properties and critical collapse determines a minimum width.
• We propose some alternative models that may better describe the shape, both for the narrow peak case and for much broader peaks where the effect of the peak shape is significant.
• We highlight the skew-lognormal and a generalised model motivated by the physics of critical collapse as the best of these possible alternatives.