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, $\Lambda$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.
Highlights
A key goal for cosmology is to characterize the accelerated cosmic expansion [1,2] and understand the underlying physics [3,4]
Observations of the expected gravitational wave (GW) signal, and an EM counterpart by ground-based telescopes, offer the exciting possibility to extend the Hubble diagram out to z ∼ 7 or higher [38,39]. This is the possibility we explore: the ability of deep-redshift standard sirens observed by Laser Interferometer Space Antenna (LISA) to validate or refute the expansion history inferred by the quasar Hubble diagram [13]
II we introduce the quasar Hubble diagram constructed with quasar observations and we briefly summarize the main steps to reproduce the results found in Ref. [13]
Summary
A key goal for cosmology is to characterize the accelerated cosmic expansion [1,2] and understand the underlying physics [3,4]. Risaliti and Lusso [13] analyzed a large catalog of x-ray and UV observations of quasars to calibrate this relationship and build a Hubble diagram that extends out to z ≃ 5.5 They found that their quasar sample yields distances that are in agreement with the standard, ΛCDM cosmological model at z ≲ 1.4. Observations of the expected GW signal, and an EM counterpart by ground-based telescopes, offer the exciting possibility to extend the Hubble diagram out to z ∼ 7 or higher [38,39] This is the possibility we explore: the ability of deep-redshift standard sirens observed by LISA to validate or refute the expansion history inferred by the quasar Hubble diagram [13]. The code used for the analysis is available at Ref. [44]
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