A note on the abundance of primordial black holes: Use and misuse of the metric curvature perturbation
Abstract
The formation of Primordial Black Holes (PBHs) through the collapse of large fluctuations in the early universe is a rare event. This manifests itself, for instance, through the nonGaussian tail of the formation probability. To compute such probability and the abundance of PBHs, the curvature perturbation is frequently adopted. In this note we emphasize that its use does not provide the correct PBH formation probability. Through a pathintegral approach we show that the exact calculation of the PBH abundance demands the knowledge of multivariate joint probabilities of the curvature perturbation or, equivalently, of all the corresponding connected correlators.
 Publication:

Physics Letters B
 Pub Date:
 May 2022
 DOI:
 10.1016/j.physletb.2022.137035
 arXiv:
 arXiv:2201.09008
 Bibcode:
 2022PhLB..82837035D
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 13 pages, 1 figure. v2: matching published version