Modified gravity in contemporary universe

Astronomical data in favor of cosmological acceleration and possible explanations of accelerated expansion of the universe are discussed. Main attention is paid to gravity modifications at small curvature which could induce accelerated cosmological expansion. 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 the R ²-extended gravity theory. Particle production rate by the oscillating curvature and the back reaction of particle production on the evolution of R are calculated in one-loop approximation. Possible implications of the model for cosmological creation of non-thermal dark matter are discussed.