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 (DD) relation $η(z)=D_L(z)(1+z)^{-2}/D_A(z)$, where $D_L$ and $D_A$ are the luminosity distance and angular diameter distance respectively, with a combination of observational data for $D_L$ taken from the latest Union2 SNe Ia and that for $D_A$ provided by two galaxy clusters samples compiled by De Filippis {\it et al.} and Bonamente {\it et al.}. Two parameterizations for $η(z)$, i.e., $η(z)=1+η_0z$ and $η(z)=1+η_0z/(1+z)$, are used. We find that the DD relation can be accommodated at $1σ$ confidence level (CL) for the De Filippis {\it et al.} sample and at $3σ$ CL for the Bonamente {\it et al.} sample. We also examine the DD relation by postulating two more general parameterizations: $η(z)=η_0+η_1z$ and $η(z)=η_0+η_1z/(1+z)$, and find that the DD relation is compatible with the results from the De Filippis {\it et al.} and the Bonamente {\it et al.} samples at $1σ$ and $2σ$ CLs, respectively. Thus, we conclude that the DD relation is compatible with present observations.