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

We perform a cosmological-model-independent test for the distance-duality (DD) relation (z) =DL (z) (1+z) ^-2/DA (z), where DL and DA are the luminosity distance and angular diameter distance respectively, with a combination of observational data for DL taken from the latest Union2 SNe Ia and that for DA provided by two galaxy clusters samples compiled by De Filippis et al. and Bonamente et al. . Two parameterizations for (z), i. e. , (z) =1+₀z and (z) =1+₀z/ (1+z), are used. We find that the DD relation can be accommodated at 1 confidence level (CL) for the De Filippis et al. sample and at 3 CL for the Bonamente et al. sample. We also examine the DD relation by postulating two more general parameterizations: (z) =₀+₁z and (z) =₀+₁z/ (1+z), and find that the DD relation is compatible with the results from the De Filippis et al. and the Bonamente et al. samples at 1 and 2 CLs, respectively. Thus, we conclude that the DD relation is compatible with present observations.