The gas mass fraction in galaxy clusters has been widely used to determine cosmological parameters. This method assumes that the ratio of the cluster gas mass fraction to the cosmic baryon fraction (\(\gamma (z)\)) is constant as a function 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 the underlying cosmology. For this calculation, we use a non-parametric functional form for the Hubble parameter obtained from Gaussian Process regression using cosmic chronometers. We parameterize \(\gamma (z)\) as: \(\gamma (z)= \gamma _0(1+\gamma _1 z)\) to constrain the redshift evolution. We find contradictory results between both the samples. For SPT-SZ, \(\gamma (z)\) decreases as a function of redshift (at more than 5\(\sigma \)), whereas a positive trend with redshift is found for Planck ESZ data (at more than 4\(\sigma \)). We however find that the \(\gamma _1\) values for a subset of SPT-SZ and 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 of the gas depletion factor, the \(4-5\sigma \) discrepancy reduces to \(2\sigma \).

星系团中的气体质量分数已被广泛用于确定宇宙学参数。该方法假定簇气体质量分数与宇宙重子分数的比率（\（\ gamma（z）\））是恒定的，随红移而变。在这项工作中，我们在模型中同时使用SPT-SZ和普朗克早期SZ（ESZ）群集数据，以寻找\（R_ {500} \）处\（\ gamma（z）\）的时间演化，独立的方式，无需对底层宇宙学有任何明确的依赖。对于此计算，我们对使用宇宙天文钟表从高斯过程回归中获得的哈勃参数使用非参数函数形式。我们将\（\ gamma（z）\）参数化为：\（\ gamma（z）= \ gamma _0（1+ \ gamma _1 z）\）限制红移的发展。我们发现两个样本之间存在矛盾的结果。对于SPT-SZ，\（\ gamma（z）\）作为红移的函数减小（大于5 \（\ sigma \）），而普朗克ESZ数据的红移呈正趋势（大于4 \（\ sigma \））。但是，我们发现同一红移间隔之间的SPT-SZ和Planck ESZ群集子集的\（\ gamma _1 \）值在\（1 \ sigma \）内一致。当我们在气体消耗因子的演变过程中考虑到晕圈质量的依赖时，\（4-5 \ sigma \）差异减小为\（2 \ sigma \）。