Measurement of the Hubble constant using the Dark Energy Survey Year 6 Gold galaxy catalogue and the fourth Gravitational-Wave Transient Catalogue

Gravitational wave (GW) standard sirens enable independent measurements of the Hubble constant $H_0$. In the absence of electromagnetic counterparts, the 'dark siren' method statistically correlates GW events with potential host galaxies. We present a measurement of $H_0$ using GWTC-4.0 (the fourth Gravitational-Wave Transient Catalogue) combined with the Dark Energy Survey Year 6 Gold photometric galaxy catalogue. Using the gwcosmo pipeline, we jointly infer cosmological and GW population parameters. We analyse the impact of galaxy catalogue properties on the inference, identifying significant features in the galaxy redshift distribution which can introduce biases. By restricting the galaxy catalogue to $0.05<z<0.50$ to maintain consistency with a uniform in comoving volume galaxy distribution, we obtain a result of $H_0 = 71.7^{+22.7}_{-18.3}\;\text{km}\;\text{s}^{-1}\;\text{Mpc}^{-1}$ from dark sirens and $H_0=73.1^{+11.9}_{-8.5}\;\text{km}\;\text{s}^{-1}\;\text{Mpc}^{-1}$ when combined with the bright siren GW170817. This study demonstrates the adaptation of deep galaxy catalogues for GW cosmology, highlighting key challenges and methodologies essential for maximizing the potential of next-generation galaxy surveys.