Primordial Black Hole Formation from Power Spectrum with Finite-width

TL;DR

This paper presents a new systematic method using density contrast peaks theory to accurately estimate primordial black hole abundance from a broad curvature power spectrum, addressing previous discrepancies.

Contribution

It introduces a novel approach combining window and filter functions to improve PBH abundance calculations across different mass scales.

Findings

Reduces discrepancy between peaks theory and Press-Schechter formalism.

Provides a general method applicable to broad power spectra.

Accounts for relevant perturbation scales and super-horizon contributions.

Abstract

Primordial black holes (PBHs) can form from gravitational collapse of large overdensities in the early Universe, giving rise to rich phenomena in astrophysics and cosmology. We develop a novel, general, and systematic method based on theory of density contrast peaks to calculate the abundance of PBHs for a broad power spectrum of curvature perturbations with Gaussian statistics. We introduce a window function to account for the relevant perturbation scales associated with PBHs of different masses, along with a filter function that removes unphysical contributions from super-horizon-scale overdensities. While some uncertainties remain due to the limited understanding of the nonlinear collapse process, our approach substantially reduces the discrepancy previously observed between peaks theory and the Press-Schechter formalism.