Possibility of realizing weak gravity in redshift space distortion measurements

TL;DR

This paper explores the theoretical possibility of achieving weaker gravity than General Relativity within modified gravity frameworks, analyzing perturbations and comparing models with observational data from redshift-space distortions and weak lensing.

Contribution

It derives conditions for realizing weak gravity in Horndeski and beyond-Horndeski theories, and presents a concrete dark energy model tested against observational data.

Findings

Weak gravity can be realized in beyond-Horndeski theories while satisfying stability conditions.

A specific dark energy scenario with varying tensor speed is numerically studied.

The model's predictions are confronted with redshift-space distortion and weak lensing observations.

Abstract

We study the possibility of realizing a growth rate of matter density perturbations lower than that in General Relativity. Using the approach of the effective field theory of modified gravity encompassing theories beyond Horndeski, we derive the effective gravitational coupling $G_{\rm eff}$ and the gravitational slip parameter $\eta$ for perturbations deep inside the Hubble radius. In Horndeski theories we derive a necessary condition for achieving weak gravity associated with tensor perturbations, but this is not a sufficient condition due to the presence of a scalar-matter interaction that always enhances $G_{\rm eff}$. Beyond the Horndeski domain it is possible to realize $G_{\rm eff}$ smaller than Newton's gravitational constant $G$, while the scalar and tensor perturbations satisfy no-ghost and stability conditions. We present a concrete dark energy scenario with varying $c_{\rm t}$ and numerically study the evolution of perturbations to confront the model with the observations of redshift-space distortions and weak lensing.