Constraints on amplitudes of curvature perturbations from primordial   black holes
  We calculate the primordial black hole (PBH) mass spectrum produced from a collapse of the primordial density fluctuations in the early Universe using, as an input, several theoretical models giving the curvature perturbation power spectra with large (~ 0.01 - 0.1) values at some scale of comoving wave numbers k. In the calculation we take into account the explicit dependence of gravitational (Bardeen) potential on time. Using the PBH mass spectra, we further calculate the neutrino and photon energy spectra in extragalactic space from evaporation of light PBHs, and the energy density fraction contained in PBHs today (for heavier PBHs). We obtain the constraints on the model parameters using available experimental data (including data on neutrino and photon cosmic backgrounds). We briefly discuss the possibility that the observed 511 keV line from the Galactic center is produced by annihilation of positrons evaporated by PBHs. 
Edgar Bugaev, Peter Klimai