Primordial black hole formation in matter domination

TL;DR

This paper investigates the formation of primordial black holes during an early matter-dominated era, finding that their formation is less efficient than during radiation domination and estimating their spin parameters.

Contribution

It introduces a realistic model for PBH formation thresholds considering peak shapes and growth effects, showing formation efficiency is limited during matter domination.

Findings

Effective threshold for PBH formation is larger than previously estimated.

PBHs formed during matter domination have slightly higher spin parameters.

Formation efficiency during matter domination is comparable but slightly less than during radiation domination.

Abstract

We study Primordial Black Holes (PBHs) formed by the collapse of rare primordial fluctuations during an early period of Matter Domination. The collapse threshold strongly depends on the shape of the peaks, decreasing as they become flatter and hence rarer. In the extreme limit of a top-hat perturbation, Harada, Kohri, Sasaki, Terada, and Yoo have argued that the growth of velocity dispersion prevents the formation of black holes unless the initial peak is larger than $\zeta_{\rm th} \sim \zeta_{\rm rms}^{2/5}$. Including the shape distribution of the peaks, we find that for a realistic cosmic abundance of PBHs, the effective threshold is larger, $\zeta_{\rm th} \sim \zeta_{\rm rms }^{1/10}$. And this model requires $\zeta_{\rm rms}\sim 10^{-1}$, which is much larger than the observed value at the CMB scales. Hence, PBH formation during Matter Domination is barely more efficient than Radiation Domination. We estimate the dimensionless spin parameter to be $a_{\rm rms} \sim \zeta_{\rm rms}^{7/4}\ll 1$, slightly larger than PBHs formed in Radiation Domination.