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 to reveal a deviation from the expansion
history predicted for the standard, $\Lambda$CDM cosmology. Here we show that
the Laser Interferometer Space Antenna (LISA) will efficiently test this claim
with standard sirens at high redshift, defined by the coincident gravitational
wave (GW) and electromagnetic (EM) observations of the merger of massive black
hole binaries (MBHBs). Assuming a fiducial $\Lambda$CDM cosmology for
generating mock standard siren datasets, the evidence for the $\Lambda$CDM
model with respect to an alternative model inferred from quasar data is
investigated. By simulating many realizations of possible future LISA
observations, we find that for $50\%$ of these realizations (median result) 4
MBHB standard siren measurements will suffice to strongly differentiate between
the two models, while 14 standard sirens will yield a similar result in $95\%$
of the realizations. In addition, we investigate the measurement precision of
cosmological parameters as a function of the number of observed LISA MBHB
standard sirens, finding that 15 events will on average achieve a relative
precision of 5\% for $H_0$, reducing to 3\% and 2\% with 25 and 40 events,
respectively. Our investigation clearly highlights the potential of LISA as a
cosmological probe able to accurately map the expansion of the universe at
$z\gtrsim 2$, and as a tool to cross-check and cross-validate cosmological EM
measurements with complementary GW observations.
