Constraints on Cosmic Distance Duality Relation from Cosmological   Observations
  In this paper, we use the model dependent method to revisit the constraint on the well-known cosmic distance duality relation (CDDR). By using the latest SNIa samples, such as Union2.1, JLA and SNLS, we find that the SNIa data alone can not constrain the cosmic opacity parameter $\varepsilon$, which denotes the deviation from the CDDR, $d_{\rm L} = d_{\rm A}(1+z)^{2+\varepsilon}$, very well. The constraining power on $\varepsilon$ from the luminosity distance indicator provided by SNIa and GRB is hardly to be improved at present. When we include other cosmological observations, such as the measurements of Hubble parameter, the baryon acoustic oscillations and the distance information from cosmic microwave background, we obtain the tightest constraint on the cosmic opacity parameter $\varepsilon$, namely the 68\% C.L. limit: $\varepsilon=0.023\pm0.018$. Furthermore, we also consider the evolution of $\varepsilon$ as a function of $z$ using two methods, the parametrization and the principle component analysis, and do not find the evidence for the deviation from zero. Finally, we simulate the future SNIa and Hubble measurements and find the mock data could give very tight constraint on the cosmic opacity $\varepsilon$ and verify the CDDR at high significance. 
Meng-Zhen Lv, Jun-Qing Xia
astro-ph.CO