# Equivalence Principle on Cosmological Backgrounds in Scalar-Tensor Theories

## TL;DR

This paper investigates how the equivalence principle applies in scalar-tensor theories of modified gravity and dark energy, showing it holds in de Sitter space and approximately in FRW cosmologies under certain conditions.

## Contribution

It demonstrates the validity of the equivalence principle in scalar-tensor models on cosmological backgrounds, including de Sitter and FRW universes, under specific symmetry and approximation conditions.

## Key findings

- Equivalence principle holds exactly in de Sitter universe due to symmetries.
- Weak equivalence principle is obeyed in FRW cosmologies in the quasi-static subhorizon limit.
- Estimated corrections to geodesic motion due to approximations.

## Abstract

We study the extent up to which the equivalence principle is obeyed in models of modified gravity and dark energy involving a single scalar degree of freedom. We focus on the effective field theories of dark energy describing the late time acceleration in the presence of ordinary matter species. In their covariant form these coincide with the Horndeski theories on a cosmological background with a slowly varying Hubble rate and a time-dependent scalar field. We show that in the case of an exactly de Sitter universe both the weak and strong equivalence principles hold. This occurs due to the combination of the shift symmetry of the scalar and the time translational invariance of de Sitter space. When generalized to Friedmann--Robertson--Walker cosmologies (FRW) we show that the weak equivalence principle is obeyed for test particles and extended objects in the quasi-static subhorizon limit. We do this by studying the field created by an extended object moving in an FRW background as well as its equation of motion in an external gravitational field. We also estimate the corrections to the geodesic equation of the extended object due to the approximations made.