Unified description of screened modified gravity

We consider modified gravity models driven by a scalar field whose effects are screened in high density regions due to the presence of nonlinearities in its interaction potential and/or its coupling to matter. Our approach covers chameleon, f(R) gravity, dilaton and symmetron models and allows a unified description of all these theories. We find that the dynamics of modified gravity are entirely captured by the time variation of the scalar field mass and its coupling to matter evaluated at the cosmological minimum of its effective potential, where the scalar field has sat since an epoch prior to big bang nucleosynthesis. This new parametrization of modified gravity allows one to reconstruct the potential and coupling to matter and therefore to analyze the full dynamics of the models, from the scale dependent growth of structures at the linear level to nonlinear effects requiring N-body simulations. This procedure is illustrated with explicit examples of reconstruction for chameleon, dilaton, f(R) and symmetron models.