Massive black hole binaries in LISA: constraining cosmological parameters at high redshifts

One of the scientific objectives of the Laser Interferometer Space Antenna (LISA) is to probe the expansion of the Universe using gravitational wave observations. Indeed, as gravitational waves from the coalescence of a massive black hole binary (MBHB) carry direct information of its luminosity distance, an accompanying electromagnetic (EM) counterpart can be used to determine its redshift. This method of $bright$ $sirens$, when applied to LISA, enables one to build a gravitational Hubble diagram to high redshift. In this work, we forecast the ability of LISA-detected MBHB bright sirens to constrain cosmological models. The expected EM emission from MBHBs can be detected up to redshift $z\sim 7$ with future astronomical facilities, and the distribution of MBHBs with detectable counterpart peaks at $z\sim 2-3$. Therefore, we propose several methods to leverage the ability of LISA to constrain the expansion of the Universe at $z\sim 2-3$, a poorly charted epoch in cosmography. We find that the most promising method consists in using a model-independent approach based on a spline interpolation of the luminosity distance-redshift relation: in this case, LISA can constrain the Hubble parameter at $z\sim2-3$ with a relative precision of at least $10\%$.