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

Abstract

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 $2\sigma$.

15 pages, 8 figures. Accepted for publication in EPJC

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• A search for the variation of speed of light using galaxy cluster gas mass fraction measurements
• A test of the standard dark matter density evolution law using galaxy clusters and cosmic chronometers
• Low redshift calibration of the Amati relation using galaxy clusters
• Probing the dark matter density evolution law with large scale structures
• Galaxy clusters, cosmic chronometers and the Einstein equivalence principle
• Comparison of $\Lambda$CDM and $R_h=ct$ with updated galaxy cluster $f_{gas}$ measurements using Bayesian inference