The Decay of Dark-Matter Inflatons Can Produce Very Energetic Cosmic   Rays
  We have shown that inflatons with a mass which is calculated to be of the order of $10^{10}\GeV$ can constitute a dominant part of dark matter. They can decay uniquely into a neutrino and antineutrino with a lifetime calculated to be greater than the present age of the universe. We show here that these neutrinos can give rise to a localized bump in the primary energy spectrum of extensive air showers. The structure would appear above the sharply-falling spectrum at the expected GZK cut-off energy for primary protons $\sim 5\times 10^{19}\GeV$. The flux which is necessary to compensate for the small cross section is, in principle, attainable, with distant structures also as possible significant sources, and such events might be observed in present experiments. 
Saul Barshay and Georg Kreyerhoff