Primordial black holes and smooth coarse-graining in excursion set theory

TL;DR

This paper explores how smooth coarse-graining affects the primordial black hole mass function within the excursion-set formalism, emphasizing the importance of noise correlations in predicting PBH abundance.

Contribution

It demonstrates the impact of correlated stochastic noise due to smooth coarse-graining on the PBH mass function, providing new insights into the role of noise correlations.

Findings

Correlated noise influences the PBH mass distribution.

Maximum of the mass function is linked to threshold exceedance probability.

Smooth coarse-graining affects predictions of PBH abundance.

Abstract

The excursion-set formalism enables us to infer the mass distribution of collapsed objects, such as primordial black holes (PBHs), by the language of stochastic processes. Within the framework, this article investigates how a smooth coarse-graining procedure affects the resulting PBH mass function. As a demonstrative example, we employ a Gaussian window function, for which the stochastic noise becomes fully correlated across scales. It is found that these correlated noises result in a mass function of PBHs, whose maximum and its neighbourhood are predominantly determined by the probability that the density contrast exceeds a given threshold at each mass scale. Our results clarify the role of noise correlations induced by smooth coarse-graining and highlight their importance in predicting the abundance of PBHs.