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The gas mass fraction in galaxy clusters has been widely used to determinecosmological parameters. This method assumes that the ratio of the cluster gasmass fraction to the cosmic baryon fraction ($\gamma(z)$) is constant as afunction of redshift. In this work, we look for a time evolution of $\gamma(z)$at $R_{500}$ by using both the SPT-SZ and Planck Early SZ (ESZ) cluster data,in a model-independent fashion without any explicit dependence on theunderlying cosmology. For this calculation, we use a non-parametric functionalform for the Hubble parameter obtained from Gaussian Process regression usingcosmic chronometers. We parameterize $\gamma(z)$ as: $\gamma(z)=\gamma_0(1+\gamma_1 z)$ to constrain the redshift evolution. We findcontradictory results between both the samples. For SPT-SZ, $\gamma (z)$decreases as a function of redshift (at more than 5$\sigma$), whereas apositive trend with redshift is found for Planck ESZ data (at more than4$\sigma$). We however find that the $\gamma_1$ values for a subset of SPT-SZand Planck ESZ clusters between the same redshift interval agree to within$1\sigma$. When we allow for a dependence on the halo mass in the evolution ofthe gas depletion factor, the $4-5\sigma$ discrepancy reduces to $2\sigma$.

A model-independent test of the evolution of gas depletion factor for SPT-SZ and Planck ESZ clusters