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A generic second-order scalar-tensor theory contains a nonlinear derivativeself-interaction of the scalar degree of freedom $\phi$ \`{a} la Galileonmodels, which allows for the Vainshtein screening mechanism. We investigatethis effect on subhorizon scales in a cosmological background, based on themost general second-order scalar-tensor theory. Our analysis takes into accountall the relevant nonlinear terms and the effect of metric perturbationsconsistently. We derive an explicit form of Newton's constant, which in generalis time-dependent and hence is constrained from observations, as suggestedearlier. It is argued that in the most general case the inverse-square lawcannot be reproduced on the smallest scales. Some applications of our resultsare also presented.

Vainshtein screening in a cosmological background in the most general second-order scalar-tensor theory