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The ratio of baryonic to dark matter densities is assumed to have remainedconstant throughout the formation of structure. With this, simulations showthat the fraction f_gas(z) of baryonic mass to total mass in galaxy clustersshould be nearly constant with redshift z. However, the measurement of thesequantities depends on the angular distance to the source, which evolves with zaccording to the assumed background cosmology. An accurate determination off_gas(z) for a large sample of hot (kT_e > 5 keV), dynamically relaxed clusterscould therefore be used as a probe of the cosmological expansion up to z < 2.The fraction f_gas(z) would remain constant only when the "correct" cosmologyis used to fit the data. In this paper, we compare the predicted gas massfractions for both LCDM and the R_h=ct Universe and test them against the 3largest cluster samples. We show that R_h=ct is consistent with a constantf_gas in the redshift range z < 2, as was previously shown for the referenceLCDM model (with parameter values H_0=70 km/s/Mpc, Omega_m=0.3 and w_de=-1).Unlike LCDM, however, the R_h=ct Universe has no free parameters to optimize infitting the data. Model selection tools, such as the Akaike InformationCriterion (AIC) and the Bayes Information Criterion (BIC), therefore tend tofavour R_h=ct over LCDM. For example, the BIC favours R_h=ct with a likelihoodof ~95% versus ~5% for LCDM.

Constancy of the Cluster Gas Mass Fraction in the R_h=ct Universe