Cosmic rays from annihilation of heavy dark matter particles

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. The 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 the assumption of homogeneous energy density, the high density DM clump in the galactic center, the cloud of DM in the Galaxy with realistic density distribution, and high density clumps of DM in the Galaxy. Possible resonance annihilation of $f\overline{f}$ into energetic light particles is considered. We have shown that the proposed scenario can successfully explain the origin of the ultrahigh energy flux of cosmic rays where canonical astrophysical mechanisms are not operative.