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