Constraints on diffuse neutrino background from primordial black holes

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Abstract
We calculate the energy spectra and fluxes of electron neutrinos emitted by the evaporation of primordial black holes (PBHs) formed by a blue power-law spectrum of primordial density fluctuations in the early universe. In the calculations of the neutrino spectra, the spectral index of density fluctuations and the reheating temperature are used as free parameters and the absorption of neutrinos during propagation in space is taken into account. We obtain the bounds on the spectral index assuming the validity of the standard picture of gravitational collapse and using the available data of several atmospheric and solar neutrino experiments. The comparison of our results with previous constraints (which had been obtained using the diffuse photon background data) shows that such bounds are quite sensitive to the assumed form of the initial PBH mass function.

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