2025MNRAS.542.3346B

In this paper, we explore the possibility of using galaxy cluster catalogues to provide redshift support for a gravitational-wave dark standard siren measurement of the Hubble constant $H_0$. We adapt the cosmology inference pipeline gwcosmo to handle galaxy cluster catalogues. Together with binary black holes from the Third Gravitational-Wave Transient Catalogue (GWTC-3), we use galaxy cluster data from the Second Planck Catalogue of Sunyaev-Zel'dovich Sources (PSZ2) and the eROSITA All Sky Survey (eRASS) catalogues. With these catalogues, we obtain $H_0 = 77^{+10}_{-10}$ and $81^{+8}_{-8} \, \text{km} \, \text{s}^{-1} \,\text{Mpc}^{-1}$, respectively, which demonstrates improvements on precision by factors of 10 per cent and 38 per cent, respectively over the traditional galaxy catalogue result. This exploratory work paves the way towards precise and accurate cosmography making use of distant compact binary mergers from upcoming observing runs of the LIGO-Virgo-KAGRA detector network and future gravitational-wave observatories.