Current and future constraints on cosmology and modified gravitational\n wave friction from binary black holes

In this proceedings, we are interested in dark gravitational wave standard\nsirens and their use for cosmology and for constraining modified gravity\ntheories. Due to the extra friction term introduced in their propagation\nequation those theories predict different luminosity distances for\nelectromagnetic and gravitational waves (GWs). This effect can be parametrized\nby the two variables $\\Xi_0$ and $n$, that can be measured from gravitational\nwave observations, and specifically from the binary black hole (BBH) mergers\ndetected by LIGO and Virgo. By fitting jointly BBH population models in mass\nand redshift, the cosmological parameters, and the modified GW luminosity\ndistance to $\\sim$ 60 signals observed during the first three LIGO/Virgo\nobservation runs, we conclude that general relativity is consistently the\npreferred model. The future observation runs O4 and O5 are also considered.\nUsing the same approach, we forecast a measurement uncertainty on the modified\ngravity parameter $\\Xi_0$ of $51\\%$ with O4, and $20\\%$ with O4 and O5,\nrespectively if GR is the correct theory of gravity. However, we underline that\nthere are strong correlations between astrophysical, cosmological and modified\ngravity parameters, possibly leading to bias if wrong priors are assumed.\n