Measuring the Curvature of the Universe with Gravitational Waves

Gravitational-wave standard sirens open new possibilities for precision cosmology. We aim to measure how well next-generation detectors can measure the cosmic expansion and geometry via the luminosity distance to gravitational-wave events, using a population of intermediate black hole binaries (IMBH) and binary neutron stars (BNS) as bright sirens. IMBH binaries have a good possibility of being formed in dense environments, such as in the disks of Active Galactic Nuclei (AGN), making electromagnetic counterparts likely. Building on previous studies focusing on flat LambdaCDM, we extend the analysis to non-flat cosmologies to constrain the curvature parameter Ωk, in addition to the Hubble parameter and the dark matter density parameter, Ωm. We perform an injection study of IMBH binaries with masses from either GW190521 or GW231123, and BNSs with masses sampled from a double Gaussian distribution, using a Fisher matrix approach implemented in the GWFish framework. The spins are sampled uniformly on a sphere, the redshift distribution is obtained from a Madau-Dickinson star formation rate density, and the other extrinsic parameters are sampled uniformly on their respective domains. We conduct a multiband study with next-generation detectors, which are sensitive in LIGO's band like Einstein Telescope (ET), Cosmic Explorer (CE), the millihertz detector LISA, and the decihertz detector Lunar Gravitational Wave Antenna (LGWA), with the following combinations: (1) ET+ CE1 + CE2, (2) ET+ CE1 + CE2 + LISA, (3) ET+ CE1 + CE2 + LGWA. Our results indicate that we'll be able to constrain the Hubble parameter to ~0.3% for all detector networks. Additionally, we will be able to constrain Ωm to 6.2%, 5.2%, and 5.6% for the three detector networks, respectively. Furthermore, the error in Ωk will be ~0.016 for all three detector networks. We note that LISA and LGWA don't have a significant contribution to constraining these parameters, as their SNRs are much lower than the SNRs of ET or CEs.