Résumé
Phys.Rev. D67 (2003) 024024 We perform an accurate computation of the production rate for primordial black holes (PBHs). The reason is that the underlying mass variance had been overestimated systematically, as was shown recently. For scale-free powerlaw primordial spectra, and for a Universe with critical density, the mass variance is less than 34% of its value thought earlier for the spectral index in the range1≤ n≤ 1.3 . We then extend our study to spectra with a characteristic scale and find the accurate shape of the corresponding mass variance. For a pure step in the primordial spectrum, the step in the variance is smoothed around the characteristic scalek_(s) . For a spectrum with large oscillations neark_(s) , we find a pronounced bump in the variance. This could yield a significant part of the cold dark matter in the form of PBHs with massMin the range5× 10¹⁵ \rm g≲ M ≲ 10²¹ \rm g .