High energy cosmic rays from neutrinos -: art. no. 123003

We address a class of models in which neutrinos, having a small mass, originate the highest energy cosmic rays interacting with the relic cosmic neutrino background. Assuming lepton number symmetry and an enhanced neutrino density in arbitrary size clusters (halos), we make an analytical calculation of the required neutrino fluxes. We show that the parameter space for these models is heavily constrained by horizontal air shower searches. Marginal room is left for models with exceptionally flat neutrino spectral indices, neutrino masses in the 0.1 epsilon V range and supercluster scale halos of order 50 Mpc size. Our constraints do not apply to models with lepton number asymmetry.