Testing the quasar Hubble diagram with LISA standard sirens

Quasars have recently been used as an absolute distance indicator, extending the Hubble diagram to high redshift reveal a deviation from expansion history predicted for standard, $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology. Here we show that Laser Interferometer Space Antenna (LISA) will efficiently test this claim with standard sirens at redshift, defined by coincident gravitational wave (GW) and electromagnetic (EM) observations of merger massive black hole binaries (MBHBs). Assuming fiducial cosmology generating mock siren data sets, evidence model respect alternative inferred quasar is investigated. By simulating many realizations possible future LISA observations, find 50% these (median result) four MBHB measurements suffice strongly differentiate between two models, while 14 yield similar result in 95% realizations. In addition, investigate measurement precision cosmological parameters function number observed sirens, finding 15 events on average achieve relative 5% ${H}_{0}$, reducing 3% 2% 25 40 events, respectively. Our investigation clearly highlights potential probe able accurately map Universe $z\ensuremath{\gtrsim}2$, tool cross-check cross-validate EM complementary GW observations.