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

TL;DR

This paper studies how Vainshtein screening operates in the most general second-order scalar-tensor theories within a cosmological background, deriving a time-dependent Newton's constant and discussing the limitations of reproducing inverse-square law at small scales.

Contribution

It provides a comprehensive analysis of Vainshtein screening in the broadest class of second-order scalar-tensor theories, including all nonlinear and metric perturbation effects.

Findings

Newton's constant becomes time-dependent in these theories

Inverse-square law cannot hold at the smallest scales in the most general case

Explicit forms of the modified gravitational interactions are derived

Abstract

A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom $\phi$ \`{a} la Galileon models, which allows for the Vainshtein screening mechanism. We investigate this effect on subhorizon scales in a cosmological background, based on the most general second-order scalar-tensor theory. Our analysis takes into account all the relevant nonlinear terms and the effect of metric perturbations consistently. We derive an explicit form of Newton's constant, which in general is time-dependent and hence is constrained from observations, as suggested earlier. It is argued that in the most general case the inverse-square law cannot be reproduced on the smallest scales. Some applications of our results are also presented.