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

Understand

We carry out a test of the cosmic distance duality relation using a sample of 52 SPT-SZ clusters, along with X-ray measurements from XMM-Newton.

• To carry out this test, we need an estimate of the luminosity distance ($D_L$) at the redshift of the cluster.
• For this purpose, we use three independent methods: directly using $D_L$ from the closest Type Ia Supernovae from the Union 2.1 sample, non-parametric reconstruction of $D_L$ using the same Union 2.1 sample, and finally using $H(z)$ measurements from cosmic chronometers and reconstructing $D_L$ using Gaussian Process regression.
• We use four different functions to characterize the deviations from CDDR.