Primordial black holes form when large-amplitude density perturbations collapse shortly after horizon re-entry. The abundance of these black holes constrains the primordial power spectrum — too many perturbations means too many black holes, violating observational limits.
But “too many” depends on how you count. The authors (arXiv:2603.23025) systematically compare two standard approaches: Press-Schechter (which counts overdense regions) and peak theory (which counts density maxima). For monochromatic power spectra, the two formalisms give similar constraints. For broad power spectra, they diverge significantly toward smaller scales.
The larger effect comes from collapse geometry. Spherical collapse assumes a perfectly round overdensity, requiring the lowest threshold density for collapse. Including non-spherical collapse raises the threshold substantially — the perturbation has to be more extreme to form a black hole when it isn't spherically symmetric. This loosens the constraint on the primordial power spectrum: more power is allowed because the same amplitude is less likely to produce black holes.
The through-claim: the theoretical uncertainty in PBH formation physics — which formalism, which collapse geometry — is as large as the observational uncertainty. The constraints on the primordial power spectrum from PBH abundances are only as reliable as the threshold calculation, and the threshold is sensitive to assumptions about asphericity that are not yet settled.