It is commonly accepted that high energy cosmic rays up to 100 EeV can be produced in catastrophic astrophysical processes. However the source of a few observed events with higher energies remains mysterious. We propose that they may originate from decay or annihilation of ultra heavy particles of dark matter. Such particles naturally appear in some models of modified gravity related  to Starobinsky inflation. Applications to the high energy neutrino events observed at IceCube are also discussed.

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Elena Arbuzova