First measurement of the Hubble constant from gravitational wave-galaxy cross-correlations

We measure for the first time the Hubble constant ($H_0$) from the cross-correlation of galaxies and gravitational waves (GW), by applying the $\mathit{\text{Peak}}\mathit{\text{Sirens}}$ method. This method consists of finding the peak of the 3D angular cross-spectrum $C_{\mathrm{\ell }}(z,D_L)$ between the galaxy redshifts ($z$) and the GW luminosity distances ($D_L$). Using two GW events from the GWTC-3.0 catalog and the GLADE+ galaxy catalog, we make the first detection of the cross-correlation peak at $5.9\sigma$ confidence. This signal comes mostly from the best localized event in the catalog, GW190814, which alone provides a $3.4\sigma$ significance. Adding also the multimessenger event GW170817, but without using its known redshift, we find $H_0=67_{-15}^{+18}$ km s${}^{-1}$Mpc${}^{-1}$ and the first observational constraint on the GW bias, $b_{\mathrm{g}\mathrm{w}}<4.3$ at 95% CI. These measurements set the stage for future novel cosmological constraints with this technique.