Constraints on the Cosmic Expansion Rate Using the DECam Local Volume Exploration Survey and the Fifth Gravitational Wave Transient Catalog

Gravitational-wave standard sirens provide a calibration-free measure of distances, offering important input on the long-standing tension between early- and late-Universe measurements of the Hubble constant ($H_0$). In the absence of an electromagnetic counterpart, the dark siren method can be employed to statistically correlate a gravitational wave event's localization with a galaxy catalog of potential hosts. We present a measurement of the Hubble constant using the DECam Local Volume Exploration Survey Data Release 3 and the fifth Gravitational-Wave Transient Catalog. Applying the dark siren method to a large, photometrically heterogeneous footprint required revised catalog-construction choices: a faint apparent-magnitude threshold ($m_r<20$) to control known photometric-redshift bias, a bright apparent-magnitude threshold ($m_r>15.5$) to exclude saturated sources, implementation of an evolving luminosity function parameterization, and de-biasing survey regions based on survey depth and photometric redshift precision. With these choices applied to DELVE, we obtain $H_0= 67.4^{+13.0}_{-11.2}\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$ from dark sirens alone, and $H_0= 70.6^{+8.7}_{-7.0}\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$ when combined with the bright siren GW170817. We test other galaxy catalog configuration choices, and find subdominant influence from photometric band choice and luminosity function parameterization on the final $H_0$ posterior. Our results demonstrate that extending the dark siren method to wider-area, non-uniform galaxy surveys is feasible and provides additional constraining power on $H_0$ relative to the spectral siren method, opening the door for analyses with forthcoming galaxy catalogs from LSST, Euclid, and Roman.