Testing the $R_{\rm h}=ct$ Universe Jointly with the Redshift-dependent Expansion rate and Angular-diameter and Luminosity Distances

Abstract: We use three different data sets, specifically $H(z)$ measurements from cosmic chronometers, the HII-galaxy Hubble diagram, and reconstructed quasar-core angular-size measurements, to perform a joint analysis of three flat cosmological models: the $R_{\rm h}=ct$ Universe, $\Lambda$CDM, and $w$CDM. For $R_{\rm h}=ct$, the 1$\sigma$ best-fit value of the Hubble constant $H_0$ is $62.336\pm1.464$ $\mathrm{km \ s^{-1} \ Mpc^{-1}}$, which matches previous measurements ($\sim 63$ $\mathrm{km \ s^{-1} \ Mpc^{-1}}$) based on best fits to individual data sets. For $\Lambda$CDM, our inferred value of the Hubble constant, $H_0=67.013\pm2.578$ $\mathrm{km \ s^{-1} \ Mpc^{-1}}$, is more consistent with the ${\it Planck}$ optimization than the locally measured value using $\mbox{Cepheid}$ variables, and the matter density $\Omega_{\rm m}=0.347\pm0.049$ similarly coincides with its ${\it Planck}$ value to within 1$\sigma$. For $w$CDM, the optimized parameters are $H_0=64.718\pm3.088$ $\mathrm{km \ s^{-1} \ Mpc^{-1}}$, $\Omega_{\rm m}=0.247\pm0.108$ and $w=-0.693\pm0.276$, also consistent with ${\it Planck}$. A direct comparison of these three models using the Bayesian Information Criterion shows that the $R_{\rm h}=ct$ universe is favored by the joint analysis with a likelihood of $\sim 97\%$ versus $\lesssim 3\%$ for the other two cosmologies.