Screening the fifth force in the Horndeski's most general scalar-tensor theories

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We study how the Vainshtein mechanism operates in the most general scalar-tensor theories with second-order equations of motion. The field equations of motion, which can be also applicable to most of other screening scenarios proposed in literature, are generally derived in a spherically symmetric space-time with a matter source. In the presence of a field coupling to the Ricci scalar, we clarify conditions under which the Vainshtein mechanism is at work in a weak gravitational background. We also obtain the solutions of the field equation inside a spherically symmetric body and show how they can be connected to exterior solutions that accommodate the Vainshtein mechanism. We apply our general results to a number of concrete models such as the covariant/extended Galileons and the DBI Galileons with Gauss-Bonnet and other terms. In these models the fifth force can be suppressed to be compatible with solar-system constraints, provided that non-linear field kinetic terms coupled to the Einstein tensor do not dominate over other non-linear field self-interactions.