Model-independent Test of the Cosmic Distance Duality Relation
Abstract
A validation of the cosmic distance duality (CDD) relation, eta(z)=(1+z)2 dA(z)/dL(z)=1, coupling the luminosity (dL) and angular-diameter (dA) distances, is crucial because its violation would require exotic new physics. We present a model-independent test of the CDD, based on strong lensing and a reconstruction of the HII galaxy Hubble diagram using Gaussian Processes, to confirm the validity of the CDD at a very high level of confidence. Using parameterizations eta(z) = 1 + eta0 z and eta(z) = 1 + eta1 z + eta2 z2, our best-fit results are eta0 = 0.0147+0.056-0.066, and eta1 = 0.1091+0.1680-0.1568 and eta2 = -0.0603+0.0999-0.0988, respectively. In spite of these strong constraints, however, we also point out that the analysis of strong lensing using a simplified single isothermal sphere (SIS) model for the lens produces some irreducible scatter in the inferred CDD data. The use of an extended SIS approximation, with a power-law density structure, yields very similar results, but does not lessen the scatter due to its larger number of free parameters, which weakens the best-fit constraints. Future work with these strong lenses should therefore be based on more detailed ray-tracing calculations to determine the mass distribution more precisely.