Cosmology beyond standard sirens: cross-correlation of gravitational waves and neutral hydrogen intensity mapping

We explore the potential of cross-correlation between gravitational wave (GW) events and neutral hydrogen (HI) intensity mapping surveys to serve as an independent cosmological probe. Focusing on the ET and the SKAO, and assuming that binary black hole mergers and HI emission are biased tracers of the underlying dark matter distribution, we use their angular auto- and cross-correlation spectra to constrain cosmological parameters. We test three different GW detector networks: ET alone, both in its $\Delta$ and 2L configuration, and ET-2L together with Cosmic Explorer. We show that the cross-correlation method, by naturally mitigating tracer-specific systematics, yields robust cosmological bounds, allowing for a sub-percent ($\sim 0.5\%$) precision on the Hubble constant $H_\mathrm{0}$. Furthermore, this approach robustly constrains the cosmic expansion history throughout the post-reionization era of the Universe and, unlike conventional standard sirens, simultaneously probes the large scale distribution of matter perturbations, achieving relative uncertainties of approximately 1.3% on the total matter density $\Omega_\mathrm{m}$ and 1.6% on the late-time clustering amplitude $\sigma_8$.