Testing the $R_{\mathrm{h}}=ct$ 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 $R_{\mathrm{h}}=ct$ Universe, $\Lambda$CDM, and $w$CDM. For $R_{\mathrm{h}}=ct$, the 1$\sigma$ best-fit value of the Hubble constant $H_0$ is $62.336\pm 1.464$ $\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, which matches previous measurements ($\sim 63$ $\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$) based on best fits to individual data sets. For $\Lambda$CDM, our inferred value of the Hubble constant, $H_0=67.013\pm 2.578$ $\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, is more consistent with the $Planck$ optimization than the locally measured value using $\mbox{Cepheid}$ variables, and the matter density ${\Omega }_{\mathrm{m}}=0.347\pm 0.049$ similarly coincides with its $Planck$ value to within 1$\sigma$. For $w$CDM, the optimized parameters are $H_0=64.718\pm 3.088$ $\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, ${\Omega }_{\mathrm{m}}=0.247\pm 0.108$ and $w=-0.693\pm 0.276$, also consistent with $Planck$. A direct comparison of these three models using the Bayesian Information Criterion shows that the $R_{\mathrm{h}}=ct$ universe is favored by the joint analysis with a likelihood of $\sim 97\%$ versus $\lesssim 3\%$ for the other two cosmologies.

arXiv comment20 pages, 4 figures, Physics of the Dark Universe, in press

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