Detection of cosmic neutrino clustering by cosmic ray spectra

We propose a method to investigate the scenario that cosmic relic neutrinos are highly clustered around stars and galaxies, or dark-matter clusters, rather than uniformly distributed in the universe. Such a scenario can be detected or constrained by the interaction of high energy cosmic ray protons and nuclei with the cosmic neutrinos. There should be observable signature in the energy spectra of cosmic ray protons and nuclei for a neutrino clustering factor beyond $10^{13}$. We provide a relation on the signature onset positions between proton and nuclei spectra, and discuss possible support from existing experiments. It is also suggested that the relative abundance of cosmic ray nuclei may detect or constrain the cosmic neutrinos with smaller clustering.