Instabilities in modified theories of gravity
  The review is devoted to consideration of possible observational consequences
of modified gravity theories, suggested for explanation of the contemporary
accelerated expansion of the universe. The major attention is paid to
F(R)-models. It is shown that in systems with rising energy density high
frequency and large amplitude oscillations of the curvature scalar, R(t), are
induced. These oscillations lead to the production of elementary particles,
which may be observed in the spectra of energetic cosmic rays. In the
background of such oscillating solutions gravitation repulsion between
finite-size objects becomes possible. Since the Lagrangian is a non-linear
function of curvature, equations of motion become of higher (4th) order and
exhibit very rich pattern of new physical effects. In particular, the evolution
of density perturbations is strongly different from that in General Relativity,
amplified due to both parametric resonance and anti-friction phenomena.
