  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.
