Constraining modified gravity with gravitational wave distance measurements

TL;DR

This paper explores how future gravitational wave measurements from the Einstein Telescope can constrain modified gravity models by analyzing deviations in GW luminosity distance, focusing on phenomenological parametrizations of dark energy and GW friction.

Contribution

It assesses the potential of the Einstein Telescope to detect deviations from General Relativity in GW propagation, especially in the context of Horndeski theories and phenomenological models.

Findings

Future GW observations can constrain modified gravity parameters.

Constraints on $f(R)$ models may be weaker than current bounds.

GW distance measurements provide an independent test of gravity theories.

Abstract

It has been shown in the literature that detections of gravitational waves (GWs) emitted by binary sources can provide measurements of luminosity distance. The events followed by electromagnetic counterparts are, then, suitable for probing the distance-redshift relation and doing cosmological parameter estimation, as well as investigating modified gravity (MG) models. In the context of effective approaches to MG equivalent to Horndeski, this GW distance differs from the standard electromagnetic luminosity distance due to the presence of a modified friction in the wave propagation. Here, we investigate how precisely the future-planned interferometer Einstein Telescope will probe such deviations from General Relativity, considering phenomenological parametrizations for both the dark energy equation of state and the GW friction. Despite being an independent test of gravity, for $f(R)$ in particular, we conclude that it may provide weaker constraints than the current available ones.