Multiband gravitational wave cosmology with stellar origin black hole binaries

Massive stellar origin black hole binaries (SBHBs), originating from stars above the pair-instability mass gap, are primary candidates for multiband gravitational wave (GW) observations. Here we study the possibility to use them as effective dark standard sirens to constrain cosmological parameters. The long lasting inspiral signal emitted by these systems is accessible by the future Laser Interferometer Space Antenna (LISA), while the late inspiral and merger are eventually detected by third generation ground-based telescopes such as the Einstein Telescope (ET). The direct measurement of the luminosity distance and the sky position to the source, together with the inhomogeneous redshift distribution of possible host galaxies, allow us to infer cosmological parameters by probabilistic means. The efficiency of this statistical method relies in high parameter estimation performances. We show that this multiband approach allows a precise determination of the Hubble constant Formula Presented with just Formula Presented detected sources. For selected SBHB population models, assuming 4 (10) years of LISA observations, we find that Formula Presented is typically determined at Formula Presented (Formula Presented), whereas Formula Presented is only mildly constrained with a typical precision of 30% (20%). We discuss the origin of some outliers in our final estimates and we comment on ways to reduce their presence.