Distance Duality in Different Cosmological Models

Abstract

At cosmological scales, one can actually measure two types of distances: luminosity distance dL and angular diameter distance dA. Within General Relativity, providing there are no processes eliminating photons from the beam, these two distances are related by the so-called distance duality relation. In this paper we used the measurements of the angular diameter distance of 38 cluster of galaxies by Bonamente et al. together with our own fits on the latest Union2 compilation of supernovae to test the distance duality relation in different cosmological models invoked to explain accelerating expansion of the Universe. Our results demonstrate that distance duality violation parameter (z) does not depend on the cosmological model assumed, but considerably depends on assumptions about mass density distribution profile of the cluster. Maximum likelihood estimates of might be interpreted as the distance duality violation. However, this effect is more pronounced for isothermal models of clusters than for the models based on hydrostatic equilibrium. This suggests that more sophisticated and accurate modeling of clusters mass density profiles is needed before the X-ray + SZ technique becomes competitive to other methods of measuring distances.