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Starting from the general Horndeski action, we derive the most generaleffective theory for scalar perturbations around flat space that allows us toscreen fifth forces via the Vainshtein mechanism. The effective theory isdescribed by a generalization of the Galileon Lagrangian, which we use to studythe stability of spherically symmetric configurations exhibiting the Vainshteineffect. In particular, we discuss the phenomenological consequences of ascalar-tensor coupling that is absent in the standard Galileon Lagrangian. Thiscoupling controls the superluminality and stability of fluctuations inside theVainshtein radius in a way that depends on the density profile of a mattersource. Particularly we find that the vacuum solution is unstable due to thiscoupling.

Effective theory for the Vainshtein mechanism from the Horndeski action