Comparison of $\mathrm{\Lambda }$CDM and $R_h=ct$ with updated galaxy cluster $f_{gas}$ measurements using Bayesian inference

We use updated gas mass fraction measurements of 44 massive dynamically relaxed galaxy clusters collated in arXiv:2111.09343 to distinguish between the standard $\mathrm{\Lambda }$CDM model and $R_h=ct$ universe. For this purpose, we use Bayesian model selection to compare the efficacy of both these cosmological models given the data. The gas mass fraction is modeled using both cosmology-dependent terms and also astrophysical parameters, which account for the variation with cluster mass and redshift. We used two different prior choices for some of the astrophysical parameters. We find a Bayes factors of 50 and 5 for $\mathrm{\Lambda }$CDM as compared to $R_h=ct$ for these two prior choices. This implies that $\mathrm{\Lambda }$CDM is favored compared to $R_h=ct$ with significance ranging from substantial to very strong.