  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.
