Testing the distance-duality relation with data from galaxy clusters and type Ia supernovae

We test the distance-duality(DD) relation by combining the angular diameter distance DA provided by two galaxy cluster samples compiled by De Filippis et al.(the elliptical β model) and Bonamente et al.(the spherical β model),and the luminosity distance DL from Constitution and Union2 type Ia supernova(SNe Ia) datasets. To obtain DL associated with the observed DA at the same redshift,we smooth the noise of the SNe Ia in a model-independent way,obtain the evolutionary curve of DL and,finally,test the DD relation. We find that the elliptical β model,when compared with the SNe Ia from the Constitution compilation,is only consistent with the DD relation at the 3σ confidence level(CL),while the spherical β model is incompatible with the DD relation at the 3σ CL. For the Union2 compilation,the De Filippis and Bonamente samples are marginally compatible with the validity of the DD relation at the 1σ and 2σ CLs,respectively.