A Note on the Abundance of Primordial Black Holes: Use and Misuse of the Metric Curvature Perturbation

Understand

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 non-Gaussian 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.