Test of the cosmic distance duality relation for arbitrary spatial curvature

The cosmic distance duality relation (CDDR), eta(z) = (1 + z)(2)d(A)(z)/d(L)(z) = 1, is one of the most fundamental and crucial formulae in cosmology. This relation couples the luminosity and angular diameter distances, two of the most often used measures of structure in the Universe. We here propose a new model-independent method to test this relation, using strong gravitational lensing (SGL) and the high-redshift quasar Hubble diagram reconstructed with a Bdzier parametric fit. We carry out this test without pre-assuming a zero spatial curvature, adopting instead the value Omega(K) = 0.001 +/- 0.002 optimized by Planck in order to improve the reliability of our result. We parametrize the CDDR using eta(z) = I + eta(0)z, 1 + eta(1)z + eta(2)z(2), and 1 + eta(3)z/(1 + z), and consider both the SIS and non-SIS lens models for the strong lensing. Our best-fitting results are: eta(0) = -0.021(-0.048)(+0.068), eta(1) = -0.404-(+0.123)(0.090), eta(2) = 0.106(-0.034)(+0.028), and eta(3) = -0.507(-0.133)(+0.193 )or the SIS model, and eta(0) = -0.109(-0.031)(+0.044) for the non-SIS model. The measured eta(z), based on the Planck parameter Omega(K), is essentially consistent with the value (=1) expected if the CDDR were fully respected. For the sake of comparison, we also carry out the test for other values of Omega(K), but find that deviations of spatial flatness beyond the Planck optimization are in even greater tension with the CDDR. Future measurements of SGL may improve the statistics and alter this result but, as of now, we conclude that the CDDR favours a flat Universe.

Automated summary

The study introduces a new method to test the cosmic distance duality relation and finds that the formula favors a flat Universe.