Primordial Black Hole Formation and Spin in Matter Domination Revisited
Weitao Ye, Yungui Gong, Tomohiro Harada, Zhaofeng Kang, Kazunori Kohri, Daiki Saito, Chul-Moon Yoo
arXiv:2508.10070v1 Announce Type: cross
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.arXiv:2508.10070v1 Announce Type: cross
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.