Threshold for primordial black holes. II. A simple analytic prescription

Primordial black holes could have been formed in the early universe from nonlinear cosmological perturbations reentering 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 dc for primordial black hole formation. Our procedure takes into account both the nonlinearities between the Gaussian curvature perturbation and the density contrast and, for the first time in the literature, the nonlinear 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.

Automated summary

This study provides a simple prescription for calculating the threshold for primordial black hole formation based on the shape of the power spectrum on superhorizon scales. The inclusion of nonlinear effects, specifically at horizon crossing, increases the threshold value by about a factor of two compared to calculations on superhorizon scales.