Cosmology and modified gravitational wave propagation from binary black hole population models

A joint hierarchical Bayesian analysis of the binary black hole (BBH) mass function, merger rate evolution and cosmological parameters can be used to extract information on both population parameters. We extend this technique include effect modified gravitational wave (GW) propagation. discuss constraints parameter $\Xi_0$ that describes phenomenon (with $\Xi_0=1$ in General Relativity, GR) using data from GWTC-3 catalog. find $\Xi_0 = 1.2^{+0.7}_{-0.7}$ with a flat prior $\Xi_0$, 1.0^{+0.4}_{-0.8}$ uniform $\log\Xi_0$ ($68\%$ C.L., maximum posterior HDI), which only rely presence feature BBH distribution around $\sim 30-45 M_{\odot}$, are robust whether or not event GW190521 is considered an outlier population. then study more detail effects GW propagation analyses for LIGO/Virgo at design sensitivity. For given data-taking period, relative error $\Delta\Xi_0/\Xi_0$ has significant dependence fiducial value since latter strong influence detection rate. five years data, accuracy ranges 10\%$ when $\Delta\Xi_0/\Xi_0\sim 20\%$ $\Xi_0=1.8$ - large deviation GR, still consistent current limits predicted by viable models. Hubble parameter, we forecast $\Delta H_0/H_0 \sim 20\%$, $H(z)$ $\sim7\%$ pivot redshift $z_*\sim 0.8$. finally show that, if Nature described gravity theory GR $\Xi_0=1$, such as $\Xi_0=1.8$, analysing assuming produces bias inferred values scales, constant,