Extreme-Value Distributions and Primordial Black-Hole Formation

TL;DR

This paper applies extreme-value theory to primordial black-hole formation, revealing a narrower mass distribution and a vastly increased predicted abundance compared to Gaussian models, with significant implications for early universe cosmology.

Contribution

It introduces extreme-value theory as a framework for modeling primordial black-hole formation, providing new predictions for their mass distribution and abundance.

Findings

Black-hole mass function is narrower and peaks at larger masses.

Predicted abundance of primordial black holes is boosted by 10^7 times.

Extreme-value distributions significantly alter formation predictions.

Abstract

We argue that primordial black-hole formation must be described by means of extreme-value theory. This is a consequence of the large values of the energy density required to initiate the collapse of black holes in the early Universe and the finite duration of their collapse. Compared to the Gaussian description of the most extreme primordial density fluctuations, the holes' mass function is narrower and peaks towards larger masses. Secondly, thanks to the shallower fall-off of extreme-value distributions, the predicted abundance of primordial black holes is boosted by $10^{7}$ orders of magnitude when extrapolating the observed nearly scale-free power spectrum of the cosmic large-scale structure to primordial black-hole mass scales.