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

Abstract: We present a new constraint on the Hubble constant ($H_0$) from the standard dark siren method using a sample of $5$ well-covered gravitational waves (GW) alerts reported during the first part of the fourth LIGO/Virgo/KAGRA observing run and with $3$ updated standard dark sirens from third observation run in combination 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 $H_0$ posterior for $5$ new standard sirens with other $10$ previous events (using the most recent available data for the 5 novel events and updated 3 previous posteriors from O3), finding $H_0 = 70.4^{+13.6}_{-11.7}~{\rm km~s^{-1}~Mpc^{-1}}$ (68\% Confidence interval) with the catalogue method only. This result represents an improvement of $\sim 23\%$ comparing the new $15$ dark siren constrain with the previous $10$ dark siren constraint and a reduction in uncertainty of $\sim 40\%$ 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 $H_0$ of $68.0^{+4.4}_{-3.8}~{\rm km~s^{-1}~Mpc^{-1}}$, a $\sim 6\%$ precision from Standard Sirens, reducing the previous constraint uncertainty by $\sim 10\%$ .