Primordial Black Hole Formation and Spin in Matter Domination Revisited

TL;DR

This paper revisits primordial black hole formation during matter domination, calculating their mass distribution and spin, and finds that the abundance is higher and spins are generally small for narrow spectra.

Contribution

It introduces a new calculation of PBH mass distribution and abundance during matter domination using peak theory and the Zel'dovich approximation, with updated predictions.

Findings

PBH abundance scales as $eta o A_ ext{γ} \sigma_h^{*5}$ for small $\sigma_h^*$

PBH spins are very small for narrow spectra but can be larger for broader spectra

PBH mass distribution becomes monochromatic for monochromatic power spectra, with abundance about 19 times previous estimates

Abstract

In this article, we calculate the mass distribution of primordial black holes (PBHs) formed in the matter-dominated (MD) era by the peak theory. We apply the Zel'dovich approximation to track the nonlinear evolution of overdensities and compute the PBH abundance and mass function by incorporating a PBH formation criterion based on the hoop conjecture. We find that the PBH abundance $\beta$ follows the scaling law $\beta \simeq A_\gamma \sigma_h^{*5}$ for $\sigma_h^*\ll 1$. Here, $\sigma_h^*$ is the quantity that characterizes the variance of the density fluctuation at the horizon entry. We also find that, in contrast to the previous estimates, the PBH spin is very small for $\sigma_h^*\ll 1$ but could be larger for larger $\sigma_h^*$ and broader power spectra. Finally, specializing to a monochromatic power spectrum, we prove analytically that the PBH mass distribution becomes effectively monochromatic and reveal that the resultant PBH abundance is approximately 19 times the previous prediction.