Testing the quasar Hubble diagram with LISA standard sirens
Lorenzo Speri, Nicola Tamanini, Robert R. Caldwell, J. R. Gair, Benjamin Wang
Abstract
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, $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology for generating mock standard siren data sets, the evidence for the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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) four 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 $z\ensuremath{\gtrsim}2$, and as a tool to cross-check and cross-validate cosmological EM measurements with complementary GW observations.