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 CDM and the R _ { h } = ct Universe and test them against the 3 largest cluster samples [ 1 , 2 , 3 ] .
We show that R _ { h } = ct is consistent with a constant f _ { gas } in the redshift range z \lesssim 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 ( AIC ) and the Bayes Information Criterion ( BIC ) , therefore tend to favor R _ { h } = ct over \Lambda CDM .
For example , the BIC favours R _ { h } = ct with a likelihood of \sim 95 \% versus \sim 5 \% for \Lambda CDM .