Distribution of primordial black holes and 21cm signature

TL;DR

This paper investigates how primordial black hole (PBH) abundance fluctuations, following different statistical distributions depending on the primordial power spectrum, impact matter structures and how future 21cm observations can constrain PBH fractions.

Contribution

It introduces the statistical distribution of PBH numbers based on primordial density perturbations and explores their effects on matter power spectrum and 21cm signals.

Findings

PBH number fluctuations follow a log-normal distribution for moderately-tilted spectra.

Poisson distribution describes PBH fluctuations for steeply blue spectra.

Future 21cm observations can significantly constrain PBH fractions across a wide mass range.

Abstract

We show that the number of primordial black holes (PBHs) which is originated from primordial density perturbations with moderately-tilted power spectrum fluctuates following the log-normal distribution, while it follows the Poisson distribution if the spectrum is steeply blue. The log-normal, as well as the Poisson, fluctuation of the PBH number behaves as an isocurvature mode and affects the matter power spectrum and the halo mass function in a different way from those for the Poisson case. The future 21cm observation can potentially put a stronger constraint on the PBH fraction than the current one in a wide mass range, $10^{-5}M_\odot$--$10M_\odot$.