Excursion-set for Primordial Black Holes I: white noise and moving barrier
Pierre Auclair, Baptiste Blachier, Vincent Vennin

TL;DR
This paper refines the excursion-set formalism for primordial black hole formation, addressing issues with correlated noise and moving barriers, and demonstrates its robustness for realistic scenarios.
Contribution
It introduces an efficient numerical framework for first-passage-time problems with moving barriers and clarifies the role of cloud-in-cloud effects in PBH formation.
Findings
Sampling on a synchronous surface removes noise correlation issues.
The new framework efficiently solves first-passage-time problems with moving barriers.
Press-Schechter estimates can fail without boundary evolution considerations.
Abstract
In the excursion-set formalism, the mass distribution of primordial black holes (PBHs) is derived from the first-passage time of a random walk describing the density contrast as the coarse-graining scale varies. We address two recent concerns that have been raised about this approach. First, it was argued that the random walks are subject to colored (i.e. correlated over time) noise, making the first-passage-time problem cumbersome. We show that this arises from an incorrect separation of drift and noise when sampling on the Hubble-crossing surface: if Fourier modes are uncorrelated, the noise is strictly white. Moreover, sampling along the Hubble-crossing surface precludes using the density dispersion as a time variable, explaining some pathologies. Sampling instead on a synchronous surface removes both issues. This requires solving a first-passage-time problem with a moving barrier,…
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