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Cosmological and Solar-System Tests of f(R) Modified Gravity

We investigate the cosmological and the local tests of the f(R) theory of modified gravity via the observations of (1) the cosmic expansion and (2) the cosmic structures and via (3) the solar-system experiments. To fit the possible cosmic expansion histories under consideration, for each of them we reconstruct f(R), known as "designer f(R)". We then test the designer f(R) via the cosmic-structure constraints on the metric perturbation ratio Psi/Phi and the effective gravitational coupling G_eff and via the solar-system constraints on the Brans-Dicke theory with the chameleon mechanism. We find that among the designer f(R) models specified by the CPL effective equation of state w_eff, only the model closely mimicking general relativity with a cosmological constant (LambdaCDM) can survive all the tests. Accordingly, these tests rule out the frequently studied "w_eff = -1" designer f(R) models which are distinct in cosmic structures from LambdaCDM. When considering only the cosmological tests, we find that the surviving designer f(R) models, although exist for a variety of w_eff, entail fine-tuning.