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The most debated crisis in cosmology today is, perhaps, the inconsistency of the estimated value of the current expansion rate of the Universe (known as the Hubble constant, H0) by different probes using high redshift and low redshift observations. Gravitational wave (GW) emitting sources, which are routinely observed nowadays through the ground-based LIGO-Virgo-KAGRA detector network, could serve as an independent probe shedding light on this problem. Such sources, also called the "standard sirens", provide us with a direct measure of the cosmological distances through the observed gravitational wave strain. When accompanied by electromagnetic observations, the redshift of the source can be independently determined, thus offering a new avenue to probe cosmic expansion. However, the majority of the detected GW events are "dark sirens" , i.e. they do not have an associated electromagnetic signal. For such sources, one can cross-match their clustering pattern with that of the observed galaxies, since they are part of the same large-scale structure and thus, are correlated with each other through structure formation history. In this talk, I will discuss how exploring the correlation between these dark sirens and galaxies allows an unbiased inference of the Hubble constant. With the large number of such events expected in future observations, this technique will be imperative for a robust cosmological inference using GWs.