Decays of superheavy relic particles may produce extremely energetic neutrinos. Their annihilations on the relic neutrinos can be the origin of the cosmic rays with energies beyond the Greisen-Zatsepin-Kuzmin cutoff. The redshift acts as a cosmological filter selecting the sources at some particular value $z_e\pm \delta z$, for which the present neutrino energy is close to the $Z$ pole of the annihilation cross section. We predict no directional correlation of the ultrahigh-energy cosmic rays with the galactic halo. At the same time, there can be some directional correlations in the data, reflecting the distribution of matter at redshift ${z=z}_e\pm \delta z$. Both of these features are manifest in the existing data. Our scenario is consistent with the neutrino mass reported by super-Kamiokande and requires no lepton asymmetry or clustering of the background neutrinos.

• Received 6 August 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.1378