Modified gravity. Problems and observational manifestations

Abstract

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.