Equivalence Principle (EP) and Solar System Constraints on R(1± ε(R Rc)) model of Gravity

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Experiments on the violation of equivalence principle (EP) and solar system give a number of constraints in which any modified gravity model must satisfy them. We study these constraints on a kind of f(R) gravity as f(R) = R(1± ε(R Rc)). For this investigation we use of chameleon mechanism and show that a spherically body has thin-shell in this model. So that we obtain an effective coupling of the fifth force which is suppressed through a chameleon mechanism. Also, we obtain γPPN = 1 ± 1.13 ×10⁻⁵ which is agreement with experiment results. At last, we show that for Rc ρc this model is consistent with EP, thin shell condition and fifth force of chameleon mechanism for ε 10⁻¹⁴.