The gravitational-wave luminosity distance in modified gravity theories

TL;DR

Modified gravity theories alter gravitational wave propagation, affecting luminosity distances, and can be distinguished from standard cosmology using future gravitational wave observations, especially with the Einstein Telescope.

Contribution

This paper demonstrates that modifications in gravitational wave propagation dominate over dark energy effects, providing a new way to test nonlocal gravity models against mbda CDM.

Findings

Modified propagation effects can be distinguished from mbda CDM with gravitational wave data.

A few tens to hundreds of standard sirens could differentiate models depending on sensitivity.

Nonlocal gravity models fit cosmological data well and are testable with future GW observations.

Abstract

In modified gravity the propagation of gravitational waves (GWs) is in general different from that in general relativity. As a result, the luminosity distance for GWs can differ from that for electromagnetic signals, and is affected both by the dark energy equation of state $w_{\rm DE}(z)$ and by a function $\delta(z)$ describing modified propagation. We show that the effect of modified propagation in general dominates over the effect of the dark energy equation of state, making it easier to distinguish a modified gravity model from $\Lambda$CDM. We illustrate this using a nonlocal modification of gravity, that has been shown to fit remarkably well CMB, SNe, BAO and structure formation data, and we discuss the prospects for distinguishing nonlocal gravity from $\Lambda$CDM with the Einstein Telescope. We find that, depending on the exact sensitivity, a few tens of standard sirens with measured redshift at $z\sim 0.4$, or a few hundreds at $1 < z < 2$, could suffice.