  Detection of massive binary black hole (BBH) mergers at high redshifts is a
target for LISA space mission. While the individual masses of a BBH merger are
redshifted, the mass ratio of BBH mergers is independent of their redshift.
Therefore, if there is an independent correlation between the mass ratio and
redshift, such a relationship can be used to i) infer the redshift of the
merging binaries, and together with the luminosity distance measurement
($D_L$), constrain the expansion rate of the universe at high redshifts $H(z)$,
and ii) constrain models of supermassive black hole seed formation in the
universe assuming a fixed cosmology. We discuss why there is an expected
relation between the mass ratio of the massive BBHs with their redshift and
show the clues for this relation by analyzing cosmological hydrodynamical
simulations of BBH mergers. This approach opens up the possibility of directly
measuring the expansion rate at redshift $z \approx 2$ with LISA for the first
time. Moreover, we discover a trend between seed mass and mass ratio of massive
BBHs which by itself is a major result that could be exploited to constrain the
formation scenarios of supermassive BH seeds.
