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We calculate the primordial black hole (PBH) mass spectrum produced from acollapse of the primordial density fluctuations in the early Universe using, asan input, several theoretical models giving the curvature perturbation powerspectra with large (~ 0.01 - 0.1) values at some scale of comoving wave numbersk. In the calculation we take into account the explicit dependence ofgravitational (Bardeen) potential on time. Using the PBH mass spectra, wefurther calculate the neutrino and photon energy spectra in extragalactic spacefrom evaporation of light PBHs, and the energy density fraction contained inPBHs today (for heavier PBHs). We obtain the constraints on the modelparameters using available experimental data (including data on neutrino andphoton cosmic backgrounds). We briefly discuss the possibility that theobserved 511 keV line from the Galactic center is produced by annihilation ofpositrons evaporated by PBHs.

Constraints on amplitudes of curvature perturbations from primordial black holes