Upper Limits on the Cosmic Neutrino Background from Cosmic Rays

Extragalactic and galactic cosmic rays scatter with the cosmic neutrino background during propagation to Earth, yielding a flux of relic neutrinos boosted to larger energies. If an overdensity of relic neutrinos is present in galaxies, and neutrinos are massive enough, this flux might be detectable by high-energy neutrino experiments. For a lightest neutrino of mass $m_{\nu }\sim 0.1$ eV, we find an upper limit on the local relic neutrino overdensity of $\sim {10}^{13}$ and an upper limit on the relic neutrino overdensity at TXS 0506+056 of $\sim {10}^{10}$. Future experiments like GRAND or IceCube-Gen2 could improve these bounds by orders of magnitude.