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

Abstract

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 $f_{\rm gas}(z)$ 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 $f_{\rm gas}(z)$ 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 $f_{\rm gas}(z)$ 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 $R_{\rm h}=ct$ Universe and test them against the 3 largest cluster samples \cite{1,2,3}. We show that $R_{\rm h}=ct$ is consistent with a constant $f_{\rm gas}$ 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 $R_{\rm h}=ct$ 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 $R_{\rm h}=ct$ over $\Lambda$CDM. For example, the BIC favours $R_{\rm h}=ct$ with a likelihood of $\sim 95\%$ versus $\sim 5\%$ for $\Lambda$CDM.