On phenomenological parametrizations for the luminosity distance of gravitational waves

The propagation of gravitational waves offers new possibilities for testing the theory of gravity. Amongst these possibilities there is the luminosity distance of gravitational waves, $d_{gw}$. It has been proposed to study this property by means of phenomenological parametrizations, which in this work we confront to the actual predictions of Einstein-scalar-Gauss-Bonnet gravity, finding that the simplest parametrization performs better. We propose a novel parametrization that covers a wider range of models, in particular, within degenerate higher order scalar-tensor theories of gravity. Also, regarding model selection from best-fit parameters, we find that even quantities derived from $d_{gw}$ can lead to inconsistent model selection if they are treated independently. This highlights that it is essential to perform simultaneous analysis and include other types of data. We expect our findings to be relevant for future constraints on modified gravity based on the properties of standard sirens.