Modified gravity. Problems and observational manifestations
  Some models of modified gravity and their observational manifestations are
considered. It is shown, that gravitating systems with mass density rising with
time evolve to a singular state with infinite curvature scalar. The universe
evolution during the radiation dominated epoch is studied in $R^2$-extended
gravity theory. Particle production rate by the oscillating curvature is
calculated. Possible implications of the model for cosmological creation of
non-thermal dark matter are discussed.
