Effective gravitational couplings for cosmological perturbations in the most general scalar-tensor theories with second-order field equations

TL;DR

This paper derives formulas for effective gravitational couplings in the most general scalar-tensor theories with second-order equations, aiding the testing of modified gravity models against cosmological observations.

Contribution

It provides a unified framework to compute effective gravitational couplings and potentials in general scalar-tensor theories, including various dark energy models, under the quasi-static approximation.

Findings

Derived expressions for $G_{eff}$ and $\

Applied formulas to multiple dark energy models, demonstrating their utility in observational tests.

Facilitated comparison of modified gravity theories with cosmological data.

Abstract

In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.