Multiband gravitational wave cosmology with stellar origin black hole binaries

TL;DR

This paper explores using stellar origin black hole binaries as multiband gravitational wave sources to precisely measure cosmological parameters, especially the Hubble constant, through combined space and ground-based observations.

Contribution

It demonstrates the potential of multiband GW observations to accurately constrain cosmological parameters with a small number of detected sources.

Findings

H$_0$ can be measured at ~2% with 4 years of LISA data.

H$_0$ can be measured at ~1.5% with 10 years of LISA data.

Omega_m is constrained to about 20-30% precision.

Abstract

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 H$_0$ with just ${\cal O}(10)$ detected sources. For selected SBHB population models, assuming $4$ ($10$) years of LISA observations, we find that H$_0$ is typically determined at $\sim 2\%$ ($\sim 1.5\%$), whereas $\Omega_m$ 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.