Constraining scalar-tensor modified gravity with gravitational waves and large scale structure surveys

The first multi-messenger gravitational wave event has had a transformative effect on the space of modified gravity models. In this paper we study the enhanced tests of gravity that are possible with a future set of gravitational wave standard siren events. We perform MCMC constraint forecasts for parameters in Horndeski scalar-tensor theories. In particular, we focus on the complementarity of gravitational waves with electromagnetic large-scale structure data from galaxy surveys. We find that the addition of fifty low redshift (z less than or similar to 0.2) standard sirens from the advanced LIGO network offers only a modest improvement (a factor 1.1-1.3, where 1.0 is no improvement) over existing constraints from electromagnetic observations of large-scale structures. In contrast, high redshift (up to z similar to 10) standard sirens from the future LISA satellite will improve constraints on the time evolution of the Planck mass in Horndeski theories by a factor similar to 5. By simulating different scenarios, we find this improvement to be robust to marginalisation over unknown merger inclination angles and to variation between three plausible models for the merger source population.