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One of the primary scientific objectives of the Laser Interferometer SpaceAntenna (LISA) is to probe the expansion of the Universe using gravitationalwave observations. Indeed, as gravitational waves from the coalescence of amassive black hole binary (MBHB) carry direct information of the luminositydistances, an accompanying electromagnetic (EM) counterpart can be used todetermine the redshift. This method of $bright$ $sirens$ enables one to build agravitational Hubble diagram to high redshift when applied to LISA. In thiswork, we forecast the ability of LISA-detected MBHB bright sirens to constraincosmological models. As the expected EM emission from MBHBs can be detected upto redshift $z\sim 7$ with future astronomical facilities, we focus on theability of LISA to constrain the expansion of the Universe at $z\sim 2-3$, apoorly charted epoch in cosmography. We find that a model-independent approachto cosmology based on a spline interpolation of the luminositydistance-redshift relation, can constrain the Hubble parameter at $z\sim2-3$with a relative precision of at least $10\%$.

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