The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription

Abstract

Primordial black holes could have been formed in the early universe from non linear cosmological perturbations re-entering the cosmological horizon when the Universe was still radiation dominated. Starting from the shape of the power spectrum on superhorizon scales, we provide a simple prescription, based on the results of numerical simulations, to compute the threshold ${\delta }_c$ for primordial black hole formation. Our procedure takes into account both the non linearities between the Gaussian curvature perturbation and the density contrast and, for the first time in the literature, the non linear effects arising at horizon crossing, which increase the value of the threshold by about a factor two with respect to the one computed on superhorizon scales.

15 pages, 9 Figures. The second version contains minor changes

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• A Note on the Abundance of Primordial Black Holes: Use and Misuse of the Metric Curvature Perturbation
• Primordial black holes and scalar-induced gravitational waves from the perturbations on the inflaton potential in peak theory
• Non-Gaussianity effects on the primordial black hole abundance for sharply-peaked primordial spectrum
• Scalar induced gravitational waves review
• Primordial Intermediate and Supermassive Black Hole formation during the electron-positron annihilation epoch
• The hand-made tail: Non-perturbative tails from multifield inflation