High-Energy and Ultra-High-Energy Neutrinos from Primordial Black Holes

Primordial Black Holes (PBHs) are capable of emitting extremely energetic particles independent of their interactions with the Standard Model. In this work, we investigate whether PBHs evaporating in the early universe could be responsible for some of the observed high-energy neutrinos above the TeV or PeV scale in the present universe. We compute the energy spectrum of neutrinos directly emitted by PBHs with a monochromatic mass function and estimate the wash-out point, which determines the maximum energy of the spectrum. We find that the spectrum generally extends to high energies following a power law of $E_{\nu}^{-3}$ until it reaches the wash-out point, which crucially depends on the PBH mass. For PBHs of $10^{13}$ grams, the spectrum can extend up to the PeV scale, though the flux is too low for detection. We also consider an indirect production mechanism involving dark particles that are emitted by PBHs and decay into neutrinos at a much later epoch. This mechanism allows lighter (such as those in the gram to kilogram range) PBHs to produce more energetic neutrino fluxes without being washed out by the thermal plasma in the early universe. In this scenario, we find that ultra-high-energy neutrinos around or above the EeV scale can be generated, with sufficiently high fluxes detectable by current and future high-energy neutrino observatories such as IceCube and GRAND.