Constraints on coasting cosmological models from gravitational-wave standard sirens

We present the first test of coasting cosmological models with gravitational-wave standard sirens observed in the first three observing runs of the LIGO-Virgo-KAGRA detector network. We apply the statistical galaxy catalog method adapted to coasting cosmologies and infer constraints on the \(H_0\) Hubble constant for the three fixed values of the curvature parameter \(k=\left\{ -1,0,+1 \right\}\) in \(H_0^2 c^{-2}\) units. The maximum posteriors and \(68.3\%\) highest density intervals we obtained from a combined analysis of \(46\) dark siren detections and a single bright siren detection are \(H_0=\left\{68.1^{+8.5}_{-5.6},67.5^{+8.3}_{-5.2},67.1^{+6.6}_{-5.8} \right\}~\mathrm{km\ s^{-1}\ Mpc^{-1}}\), respectively. All our constraints on \(H_0\) are consistent within one sigma with the \(H_0\) measured with the differential age method, which provides a constraint on \(H_0\) in coasting cosmologies independently from \(k\). Our results constrain all cosmological models with \(a(t)\propto t\) linear expansion in the luminosity distance and redshift range of the \(47\) LIGO-Virgo detections, i.e. \(d_\mathrm{L}\lesssim 5~\mathrm{Gpc}\) and \(z\lesssim 0.8\), which practically include all (both strictly linear and quasi-linear) models in the coasting model family. As we have found, the coasting models and the \(\Lambda\)CDM model fit equally well to the applied set of gravitational-wave detections.