Diffuse Boosted Cosmic Neutrino Background

Energetic cosmic rays scatter off the cosmic neutrino background throughout the history of the Universe, yielding a diffuse flux of cosmic relic neutrinos boosted to high energies. We calculate this flux under different assumptions of the cosmic-ray flux spectral slope and redshift evolution. The non-observation of the diffuse flux of boosted relic neutrinos with current high-energy neutrino experiments already excludes an average cosmic neutrino background overdensity larger than $\sim {10}^4$ over cosmological distances. We discuss the future detectability of the diffuse flux of boosted relic neutrinos in light of neutrino overdensity estimates and cosmogenic neutrino backgrounds.