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A formula for the initial mass spectrum of primordial black holes (PBHs), which can be used for the general case of a scale dependent spectral index, and for a wide class of models of gravitational collapse, is derived. The derivation is based on the Press-Schechter formalism. A comparative analysis of different types of initial mass spectra used in concrete calculations is carried out. It is shown that densities of background radiation (, ) from PBH evaporation depend rather strongly on the type of gravitational collapse and on taking into account the spread of horizon masses at which PBHs can form. Constraints on the parameters of the primordial density perturbation amplitudes based on PBH evaporation processes and on atmospheric and solar neutrino data are obtained.
Bugaev et al. (Fri,) studied this question.