A model-independent test of the evolution of gas depletion factor for
  SPT-SZ and Planck ESZ clusters
  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 $2\sigma$.
