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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. 

ABSTRACT The current and next observation seasons will detect hundreds of gravitational waves (GWs) from compact binary systems coalescence at cosmological distances. When combined with independent electromagnetic measurements, the source redshift will be known, and we will be able to obtain precise measurements of the Hubble constant H0 via the distance–redshift relation. However, most observed mergers are not expected to have electromagnetic counterparts, which prevents a direct redshift measurement. In this scenario, one possibility is to use the dark sirens method that statistically marginalizes over all the potential host galaxies within the GW location volume to provide a probabilistic source redshift. Here we presented H0 measurements using two new dark sirens compared to previous analyses using DECam data: GW190924$$\_$$021846 and GW200202$$\_$$154313. The photometric redshifts of the possible host galaxies of these two events are acquired from the DECam Local Volume Exploration Survey (DELVE) carried out on the Blanco telescope at Cerro Tololo. The combination of the H0 posterior from GW190924$$\_$$021846 and GW200202$$\_$$154313 together with the bright siren GW170817 leads to $$H_{0} = 68.84^{+15.51}_{-7.74}\, \rm {km\, s^{-1}\, Mpc^{-1}}$$. Including these two dark sirens improves the 68  per cent confidence interval (CI) by 7  per cent over GW170817 alone. This demonstrates that the addition of well-localized dark sirens in such analysis improves the precision of cosmological measurements. Using a sample containing 10 well-localized dark sirens observed during the third LIGO/Virgo observation run, without the inclusion of GW170817, we determine a measurement of $$H_{0} = 76.00^{+17.64}_{-13.45}\, \rm {km\, s^{-1}\, Mpc^{-1}}$$.