Solar-System Constraints on f(R) Chameleon Gravity

We investigate the solar-system constraint on the f(R) theory of modified gravity with chameleon mechanism, where f(R) represents the deviation from general relativity in the gravity action. We obtain a stringent bound to a general, non-constant deviation function f(R): -10^{-15} < df/dR < 0 when R ~ 3*10^5*H0^2, and a loose bound: 0 < R*d(df/dR)/dR < 2/5 when R > 3*10^5*H0^2, by requiring the thin-shell condition in the solar system, particularly in the atmosphere of the Earth. These bounds can be conveniently utilized to test the f(R) models with given functional forms of f(R) and to obtain the constraints on the parameters therein. For demonstration we apply these bounds to several widely considered f(R) models. (H0: Hubble constant)