Eungwang Seo, Kyungmin Kim, Zhuotao Li, Justin Janquart, Rachel Gray, Martin Hendry

The disagreement between early and late Universe electromagnetic measurements of the Hubble constant, $H_0$, known as the Hubble tension, highlights the need for independent and complementary probes. Gravitational-wave events have recently emerged as such a probe for constraining cosmological parameters. $H_{0}$ inference using these events relies on sky localization and luminosity distance estimates, both of which can be significantly improved for strongly lensed events with appropriate lens modeling. In this context, we propose utilizing strong lensing of dark sirens, gravitational-wave events without identified electromagnetic counterparts, in combination with strong lensing of galaxies as a novel method for measuring $H_0$. The constant is inferred from the luminosity distances of these lensed dark sirens and the redshifts of their host galaxies, combining information from individual events to obtain statistically stronger constraints when multiple events are available. We adopt a simulated galaxy catalog, \texttt{MICECATv2}, as the basis for simulating strong lensing of galaxies and to provide the redshift information of host galaxy candidates required to infer $H_0$. We also examine the impact of galaxy catalog incompleteness on the resulting $H_0$ inference. Our results demonstrate that using only 8 strongly lensed dark sirens, analyzed with a dedicated galaxy-galaxy lensing catalog, can improve the precision of $H_{0}$ by roughly 50\% compared to 250 unlensed events.