Constancy of the cluster gas mass fraction in the R_h =ct Universe

The ratio of baryonic to dark matter densities is assumed to have remained constant throughout the formation of structure. With this, simulations show that the fraction f_gas(z) of baryonic mass to total mass in galaxy clusters should be nearly constant with redshift z. However, the measurement of these quantities depends on the angular distance to the source,which evolves with z according to the assumed background cosmology. An accurate determination of f_gas(z) for a large sample of hot (kT_e >5keV), dynamically relaxed clusters could 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 cosmology is used to fit the data. In this paper, we compare the predicted gas mass fractions for both Λ cold dark matter (ΛCDM) and the R_h =ct Universe and test them against the three largest cluster samples (LaRoque et al. 2006 Astrophys. J. 652, 917-936 (doi:10.1086/508139); Allen et al. 2008 Mon. Not. R. Astron. Soc. 383, 879-896 (doi:10.1111/j.1365-2966.2007.12610.x); Ettori et al. 2009 Astron. Astrophys. 501, 61-73 (doi:10.1051/ 0004-6361/200810878)). We show that R_h =ct is consistent with a constant f_gas in the redshift range z ≲ 2, as was previously shown for the reference ΛCDM model (with parameter values H₀ = 70kms^-1 Mpc^-1, Ω_m =0.3 and w_Λ =-1). Unlike ΛCDM, however, the R_h =ct Universe has no free parameters to optimize in fitting the data. Model selection tools, such as the Akaike information criterion and the Bayes information criterion (BIC), therefore tend to favour R_h =ct over ΛCDM. For example, the BIC favours R_h =ct with a likelihood of approximately 95% versus approximately 5% for ΛCDM.