Bayesian Comparison of the Cosmic Duality Scenarios

The cosmic distance duality relation (CDDR), $D_{\rm L}(1+z)^{-2}/D_{\rm A}=\eta=1$, 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., $\eta=\eta(z)$. 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 $\eta(z)$ functions. We show that the data here used are unable to pinpoint, with a high degree of Bayesian evidence, which $\eta(z)$ function best captures the evolution of CDDR.