COSMOLOGICAL-MODEL-INDEPENDENT TESTS FOR THE DISTANCE–DUALITY RELATION FROM GALAXY CLUSTERS AND TYPE Ia SUPERNOVA

Abstract

We perform a cosmological-model-independent test for the distance-duality\n(DD) relation $\\eta(z)=D_L(z)(1+z)^{-2}/D_A(z)$, where $D_L$ and $D_A$ are the\nluminosity distance and angular diameter distance respectively, with a\ncombination of observational data for $D_L$ taken from the latest Union2 SNe Ia\nand that for $D_A$ provided by two galaxy clusters samples compiled by De\nFilippis {\\it et al.} and Bonamente {\\it et al.}. Two parameterizations for\n$\\eta(z)$, i.e., $\\eta(z)=1+\\eta_0z$ and $\\eta(z)=1+\\eta_0z/(1+z)$, are used.\nWe find that the DD relation can be accommodated at $1\\sigma$ confidence level\n(CL) for the De Filippis {\\it et al.} sample and at $3\\sigma$ CL for the\nBonamente {\\it et al.} sample. We also examine the DD relation by postulating\ntwo more general parameterizations: $\\eta(z)=\\eta_0+\\eta_1z$ and\n$\\eta(z)=\\eta_0+\\eta_1z/(1+z)$, and find that the DD relation is compatible\nwith the results from the De Filippis {\\it et al.} and the Bonamente {\\it et\nal.} samples at $1\\sigma$ and $2\\sigma$ CLs, respectively. Thus, we conclude\nthat the DD relation is compatible with present observations.\n