Bayesian Comparison of the Cosmic Duality Scenarios

Abstract

The cosmic distance duality relation (CDDR), $D_{\mathrm{L}}(1+z{)}^{-2}/D_{\mathrm{A}}=\eta =1$, with $D_{\mathrm{L}}$ and $D_{\mathrm{A}}$, 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.

10 pages, 3 figures, 3 tables. v3: matches version published in PRD

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