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The Horndeski theory of gravity is known as the most general scalar-tensortheory with second-order field equations. Recently, it was demonstrated byGleyzes et al. that the Horndeski theory can further be generalized in such away that although field equations are of third order, the number of propagatingdegrees of freedom remains the same. We study small-scale gravity in thegeneralized Horndeski theory, focusing in particular on an impact of the newderivative interaction beyond Horndeski on the Vainshtein screening mechanism.In the absence of the quintic galileon term and its generalization, we showthat the new interaction does not change the qualitative behavior of gravityoutside and near the source: the two metric potentials coincide, $\Phi = \Psi\;(\sim r^{-1})$, while the gravitational coupling is given by the cosmologicalone and hence is time-dependent in general. We find, however, that thegravitational field inside the source shows a novel behavior due to theinteraction beyond Horndeski: the gravitational attraction is not determinedsolely from the enclosed mass and two potentials do not coincide, indicatingbreaking of the screening mechanism.

Breaking of Vainshtein screening in scalar-tensor theories beyond Horndeski