arXiv:1805.04087 [astro-ph.CO]AbstractReferencesReviewsResources
The abundance of primordial black holes depends on the shape of the inflationary power spectrum
Published 2018-05-10Version 1
In this letter, combining peak theory and the numerical analysis of gravitational collapse in the radiation dominated era, %of the early Universe, we show that the abundances of primordial blacks holes, generated by an enhancement in the inflationary power spectrum, is extremely dependent upon the shape of the peak. Given the amplitude of the power spectrum we show that the density of primordial black holes generated from a narrow peak, is exponentially smaller compared to the case of a broad peak. Specifically, for a top-hat profile of the power spectrum in Fourier space, we find that in order to consider primordial black holes as the whole of dark matter, one needs a power spectrum an order of magnitude smaller than what has been so far used. Whereas, in the case of a narrow peak, one would need a way larger power spectrum which in many cases invalidates the perturbative analysis of cosmological perturbations. Finally, we show that, although the critical collapse gives a relatively broad mass spectrum, the density of primordial black holes is essentially peaked to a single mass value.