A general, systematic peaks-theory method computes the abundance of primordial black holes formed from a broad (finite-width) power spectrum of Gaussian curvature perturbations. A window function selects the perturbation scales relevant to PBHs of a given mass and a filter function removes unphysical contributions from super-horizon-scale overdensities; applied to a log-normal spectrum (with monochromatic and high-peak limits) the method substantially reduces the long-standing discrepancy between the density-peaks calculation and the Press-Schechter estimate of the PBH mass function, with residual uncertainty from the nonlinear collapse threshold.
Cosmology / particle-astrophysics primary-research paper (Pi, Sasaki, Takhistov & Wang; JCAP09(2025)045). The authors develop a novel, general, systematic method, based on the theory of density-contr…