Hearing gravity from the cosmos: GWTC-2 probes general relativity at cosmological scales

Gravitational-wave (GW) catalogs are rapidly increasing in number, allowing for robust statistical analyses of the population of compact binaries. Nonetheless, GW inference of cosmology has typically relied on additional electromagnetic counterparts or galaxy catalogs. I present a new probe of cosmological modifications of general relativity with GW data only. I focus on deviations of the GW luminosity distance constrained with the astrophysical population of binary black holes (BBHs). The three key observables are 1) the number of events as a function of luminosity distance, 2) the stochastic GW background of unresolved binaries and 3) the location of any feature in the source mass distribution, such as the pair instability supernova (PISN) gap. Despite a priori degeneracies between modified gravity and the unknown evolution of the merger rate and source masses, a large damping of the GW amplitude could be falsifiable since as redshift grows it reduces the events and lowers the edges of the PISN gap, which is against standard astrophysical expectations. Applying a hierarchical Bayesian analysis to the current LIGO--Virgo catalog (GWTC-2), the strongest constraints to date are placed on deviations from the GW luminosity distance, finding $c_{_M}=-3.2^{+3.4}_{-2.0}$ at $68\%$ C.L., which is $\sim10$ times better than multi-messenger GW170817 bounds. These modifications also affects the determination of the BBH masses, which is crucial to accommodate the high-mass binary GW190521 away from the PISN gap. In this analysis it is found that the maximum mass of $99\%$ of the population shifts to lower masses with increased uncertainty, $m_{99\%}=46.2^{+11.4}_{-9.1}M_\odot$ at $68\%$ C.L. Testing gravity at large scales with the population of BBHs will become increasingly relevant with future catalogs, providing an independent and self-contained test of the standard cosmological model.