Constraints on some f(R) gravity models in the Palatini formalism from a time-varying gravitational constant

In this work, we studied how the relative variation of the gravitational constant vertical bar GG vertical bar(0) at the redshift z=0 restricts model parameters in Palatini f(R) gravity. According to results from the observation of big bang nucleosynthesis and the anisotropies in the cosmic microwave background radiation, the ratio that gives the general constraint condition on the f(R) model is taken to be vertical bar GG(0)< 10(-13) yr(-1). Associating with the scalar curvature at present, this constraint condition yields concrete relations among model parameters in the generalized Lambda CDM model, the logarithmic Lagrangian, and the exponential gravity model. These constraint relations which can be reconcilable with the value vertical bar GG vertical bar(0)< 10(-13) yr(-1) are plotted.