Constancy of the cluster gas mass fraction in the Rh = 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) > 5 keV), 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 Lambda cold dark matter (Lambda CDM) 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 less than or similar to 2, as was previously shown for the reference Lambda CDM model (with parameter values H-0 = 70 km s(-1) Mpc(-1), Omega(m) = 0.3 and w(Lambda) = -1). Unlike Lambda CDM, 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 Lambda CDM. For example, the BIC favours R-h = ct with a likelihood of approximately 95% versus approximately 5% for Lambda CDM.