Cosmology with standard sirens at cosmic noon

Gravitational waves (GWs) from merging black holes and neutron stars directly measure the luminosity distance to the merger, which, when combined with an independent measurement of the source's redshift, provides a novel probe of cosmology. The proposed next generation of ground-based GW detectors, Einstein Telescope and Cosmic Explorer, will detect tens of thousands of binary neutron stars (BNSs) out to cosmological distances (z >2 ), beyond the peak of the star formation rate (SFR), or "cosmic noon." At these distances, it will be challenging to measure the sources' redshifts by observing electromagnetic (EM) counterparts or statistically marginalizing over a galaxy catalog. In the absence of an EM counterpart or galaxy catalog, Ding et al. [J. Cosmol. Astropart. Phys. 04 (2019) 033], 10.1088/1475-7516/2019/04/033 showed that theoretical priors on the merger redshift distribution can be used to infer parameters in a w CDM (Cold Dark Matter) cosmology. We argue that in the BNS case, the redshift distribution will be measured by independent observations of short gamma ray bursts (GRBs), kilonovae, and known BNS host galaxies. In particular, the peak redshift will provide a clear feature to compare against the peak distance of the GW source distribution and reveal the underlying redshift-distance relation. We show that, in addition to measuring the background cosmology, this method can constrain the effects of dark energy on modified GW propagation. As a simple example, we consider the case in which the BNS rate is a priori known to follow the SFR. If the SFR is perfectly known, O (10 ,000 ) events (to be expected within a year of observation with Cosmic Explorer) would yield a subtenth percent measurement of the combination H₀^2.8Ω_M in a flat Λ CDM model. Meanwhile, fixing H₀ and Ω_M to independently inferred values, this method may enable a 5% measurement of the dark energy equation of state parameter w in a w CDM model. Fixing the background cosmology and instead probing modified GW propagation, the running of the Planck mass parameter c_M may be measured to ±0.02 . Although realistically, the redshift evolution of the merger rate will be uncertain, prior knowledge of the peak redshift will provide valuable information for standard siren analyses.