  We present the latest measurements of the Hubble parameter and of the
parameter $\Xi_0$ describing modified gravitational wave propagation, obtained
from the third gravitational wave transient catalog, GWTC-3, using the
correlation with galaxy catalogs and information from the source-frame mass
distribution of binary black holes. The latter leads to the tightest bound on
$\Xi_0$ so far, i.e. $\Xi_0 = 1.2^{+0.7}_{-0.7}$ with a flat prior on $\Xi_0$,
and $\Xi_0 = 1.0^{+0.4}_{-0.8}$ with a prior uniform in $\log\Xi_0$ (Max
posterior and $68\%$ HDI). The measurement of $H_0$ is dominated by the single
bright siren GW170817, resulting in $H_0=67^{+9}_{-6} \, \rm km \, s^{-1} \,
Mpc$ when combined with the galaxy catalog.
