Possibility of realizing weak gravity in redshift space distortion measurements

Understand

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.