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We carry out a test of the cosmic distance duality relation using a sample of52 SPT-SZ clusters, along with X-ray measurements from XMM-Newton. To carry outthis test, we need an estimate of the luminosity distance ($D_L$) at theredshift of the cluster. For this purpose, we use three independent methods:directly using $D_L$ from the closest Type Ia Supernovae from the Union 2.1sample, non-parametric reconstruction of $D_L$ using the same Union 2.1 sample,and finally using $H(z)$ measurements from cosmic chronometers andreconstructing $D_L$ using Gaussian Process regression. We use four differentfunctions to characterize the deviations from CDDR. All our results for these($4 \times 3$) analyses are consistent with CDDR to within 1$\sigma$.

A test of cosmic distance duality relation using SPT-SZ galaxy clusters, Type Ia supernovae, and cosmic chronometers