Bayesian Comparison of the Cosmic Duality Scenarios

The cosmic distance duality relation (CDDR), $D_{\rm L}(1+z)^{-2}/D_{\rm A}=η=1$, with $D_{\rm L}$ and $D_{\rm A}$, being the luminosity and angular diameter distances, respectively, is a crucial premise in cosmological scenarios. Many investigations try to test CDDR through observational approaches, even some of these ones also consider a deformed CDDR, i.e., $η=η(z)$. In this paper, we use type Ia supernovae luminosity distances and galaxy cluster measurements (their angular diameter distances and gas mass fractions) in order to perform a Bayesian model comparison between $η(z)$ functions. We show that the data here used are unable to pinpoint, with a high degree of Bayesian evidence, which $η(z)$ function best captures the evolution of CDDR.

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