Deformed Distance Duality Relations and Supernovae Dimming
  The basic cosmological distances are linked by the Etherington cosmic distance duality relation, $\eta (z) = D_{L}(z)(1+z)^{-2}/D_{A}(z) \equiv 1$, where $D_{L}$ and $D_{A}$ are, respectively, the luminosity and angular diameter distances. In order to test its validity, some authors have proposed phenomenological expressions for $\eta(z)$ thereby deforming the original Etherington's relation and comparing the resulting expressions with the available and future cosmological data. The relevance of such studies is unquestionable since any violation of the cosmic distance duality relation could be the signal of new physics or non-negligible astrophysical effects in the usually assumed perfectly transparent Universe. In this letter, we show that under certain conditions such expressions can be derived from a more fundamental approach with the parameters appearing in the $\eta(z)$ expression defining the cosmic absorption parameter as recently discussed by Chen and Kantowski. Explicit examples involving four different parametrizations of the deformation function are given. Based on such an approach, it is also found that the latest Supernova data can also be explained in the framework of a pure cold dark matter model (Einstein-de Sitter). Two different scenarios with cosmic absorption are discussed. Only if the cosmic opacity is fully negligible, the description of an accelerating Universe powered by dark energy or some alternative gravity theory must be invoked. 
J. A. S. Lima, J. V. Cunha, V. T. Zanchin
astro-ph.CO gr-qc hep-th