We compute the flux of relic neutrino background (
RνB) up-scattered by ultrahigh-energy (UHE) cosmic rays (CRs) in clusters that act as CR-reservoirs. The long trapping times of UHECRs make this flux larger than that of
RνB up-scattered by UHECRs on their way to Earth, which we also compute. We find that IceCube excludes
RνB weighted overdensities larger than
1010 in clusters, and that PUEO, RNO-G, GRAND, and IceCube-Gen2 will test values down to
108. Our treatment incorporates the momentum transfer dependence of the neutrino-nucleus cross section, deep inelastic scattering, a mixed UHECR composition, and flavor information on the up-scattered
RνB fluxes for both cases of neutrino mass spectrum with normal and inverted ordering, providing new handles to possibly disentangle the up-scattered
RνB from cosmogenic neutrinos. Published by the American Physical Society 2025