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 nonobservation of the diffuse flux of boosted relic neutrinos with current high-energy neutrino experiments already excludes an average cosmic neutrino background overdensity larger than <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo>∼</a:mo><a:msup><a:mn>10</a:mn><a:mn>4</a:mn></a:msup></a:math> 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.