LISA bright sirens as a tiebreaker among cosmologies in tension

Gravitational waves from massive black hole binaries detected by LISA will deliver luminosity distances without any astrophysical calibration, offering a probe of the expansion history independent of the cosmic distance ladder. Rather than asking how tightly LISA will constrain a single fiducial cosmology, we ask which of several mutually discrepant present-day cosmologies a future LISA dataset would render most self-consistent. We build mock catalogues of LISA bright sirens under three fiducial cosmologies drawn from datasets that participate in the current H 0 discrepancy (Planck 2018, Union3 and Pantheon+SH0ES), with a self-consistent error budget from instrumental noise, weak lensing and host peculiar velocities. We compare the posterior from the simulated LISA data alone with that of a real-data combination of Type Ia supernovae, DESI baryon acoustic oscillations, cosmic chronometers and the compressed Planck 2018 CMB, and quantify their internal tension in the (H 0,Ω m) plane, crossing each fiducial with three SN Ia compilations. The fiducial drives the tension, from 2.08σ to well beyond 5σ, while the supernova compilation changes it by at most 1.2σ. The discriminating power is strongly asymmetric: a Pantheon+SH0ES universe is inconsistent with every background we test, at a significance far in excess of 5σ and still at 3 - 5σ for the 10 - 20 events expected from recent population models, whereas the Planck 2018 and Union3 fiducials, which differ by only 0.24 km/s/Mpc in H 0, cannot be separated by any catalogue size. LISA bright sirens are therefore a sharp arbiter of the Cepheid-calibrated scenario and, on this error budget, silent between the other two.