Constraining f(R) gravity in solar system, cosmology and binary pulsar systems

The f(R) gravity can be cast into the form of a scalar-tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general f(R) gravity, using a scalar-tensor representation with the chameleon mechanism, we calculate the parametrized post-Newtonian parameters γ and β, the effective gravitational constant Geff, and the effective cosmological constant Λeff. In addition, for the general f(R) gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific f(R) models (Hu-Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.