Model selection using the HII galaxy Hubble diagram

The proposal to use HII galaxies (HIIGx) and giant extragalactic HII regions (GEHR) as standard candles to construct the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae has gained considerable support recently with the addition of five new HIIGx discovered by JWST. The updated sample of 231 sources now extends the redshift range of these objects to $z\sim 7.5$, mapping the Universe's expansion over $95\%$ of its current age. In this {\it Letter} we use these sources for model selection, and show that the $R_{\rm h}=ct$ universe is strongly favored by this probe over both flat-$\Lambda$CDM and $w$CDM, with relative Bayesian Information Criterion probabilities of, respectively, $91.8\%$, $7.4\%$ and $0.8\%$. A possible caveat with these results, however, is that an unknown dispersion, $\sigma_{\rm int}$, in the HIIGx standard candle relation can weaken the model comparisons. We find that the inclusion of $\sigma_{\rm int}$ as an additional, optimizable parameter makes the likelihoods of flat-$\Lambda$CDM and $R_{\rm h}=ct$ about equal, though at the expense of creating $\sim 2.5\sigma$ tension between our inferred matter density $\Omega_{\rm m}$ and its {\it Planck}-optimized value.