  The origin of the ultra high energy cosmic rays via annihilation of heavy
stable, fermions "f", of the cosmological dark matter (DM) is studied. The
particles in question are supposed to be created by the scalaron decays in
$R^2$ modified gravity. Novel part of our approach is the assumption that the
mass of these carriers of DM is slightly below than a half of the scalaron
mass. In such a case the phase space volume becomes tiny. It leads to
sufficiently low probability of "f" production, so their average cosmological
energy density could be equal to the observed energy density of dark matter.
Several regions of the universe, where the annihilation could take place, are
studied. They include the whole universe under assumption of homogeneous energy
density, the high density DM clump in the galactic centre, the cloud of DM in
the Galaxy with realistic density distribution, and high density clusters of DM
in the Galaxy. Possible resonance annihilation of $f \bar f$ into energetic
light particle is considered. We have shown that the proposed scenario can
successfully explain the origin of the ultrahigh energy flux of cosmic rays
where the canonical astrophysical mechanisms are not operative.
