  The search for supersymmetric partners at Large Hadron Collider revealed
negative result. Though, strictly speaking, it does not exclude low energy
supersymmetry, but still it leads to strong constraints of the parameter space.
Therefore the search for supersymmetric particles at higher energies becomes of
interest. It is shown that in $R^2$-modified cosmology heavy particles with the
interaction strength typical for supersymmetry could be promising candidates
for carriers of dark matter. We consider the heating of the Universe at the
post-inflationary stage via particle production by oscillating curvature scalar
(scalaron). The bounds on the masses of dark matter particles are obtained for
different dominant decay modes of the scalaron. Possible impact of superheavy
particle decays on the spectrum of ultra high energy cosmic rays is discussed.
