A dark standard siren measurement of the Hubble constant following LIGO/Virgo/KAGRA O4a and previous runs

We present a new constraint on the Hubble constant (H₀) from the standard dark siren method using a sample of five well-covered gravitational wave (GW) alerts reported during the first part of the fourth observing run of the Laser Interferometer Gravitational-Wave Observatory (LIGO), the Virgo and Kamioka Gravitational Wave Detector (KAGRA) collaborations (LVK) and with three updated standard dark sirens from third observation run in combination with the previous constraints from the first three runs. Our methodology relies on the galaxy catalogue method alone. We use a deep learning method to derive the full probability density estimation of photometric redshifts using the Legacy Survey catalogues. We add the constraints from well localized binary black hole mergers to the sample of standard dark sirens analysed in our previous work. We combine the H₀ posterior for 5 new standard sirens with other 10 previous events (using the most recent available data for the five novel events and updated three previous posteriors from O3), finding H₀ = 70.4+13.6-11.7~ km~s⁻¹~Mpc⁻¹ (68 per cent confidence interval) with the catalogue method only. This result represents an improvement of ~ 23~\ per\ cent comparing the new 15 dark siren constraints with the previous 10 dark siren constraints and a reduction in uncertainty of ~ 40~\ per\ cent from the combination of 15 dark and bright sirens compared with the GW170817 bright siren alone. The combination of dark and bright siren GW170817 with recent jet constraints yields H₀ of 68.0+4.4-3.8~ km~s⁻¹~Mpc⁻¹, a ~ 6~\ per\ cent precision from standard sirens, reducing the previous constraint uncertainty by ~ 10~\ per\ cent.