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A Note on the Abundance of Primordial Black Holes: Use and Misuse of the Metric Curvature Perturbation
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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. Through a path-integral 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.
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Cited by 2 Pith papers
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Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer
A Bayesian analysis shows that a future sub-solar PBH detection would make the primordial SIGW interpretation of PTA data favored over the SMBH interpretation, but this preference is driven by the detection prior.
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Primordial Black Hole Formation from the Upward Step Model: Avoiding Overproduction
In upward-step inflation, a non-Gaussian cutoff in curvature perturbations sharply suppresses type-I primordial black hole abundance for h above about 5.9, easing PTA overproduction constraints.
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