Testing the distance-duality relation with a combination of cosmological distance observations

We propose an accurate test of the distance-duality (DD) relation, η = DL(z)(1 + z)-2/DA(z) = 1 (where DL and DA are the luminosity distances and angular diameter distances, respectively), with a combination of cosmological observational data of Type Ia Supernovae (SNe Ia) from the Union2 set and the galaxy cluster sample under an assumption of the spherical model. In order to avoid bias brought on by redshift non-coincidence between observational data and to consider redshift error bars of both clusters and SNe Ia in the analysis, we carefully choose the SNe Ia points which have the minimum acceptable redshift difference of the galaxy cluster sample (|Δz|min = σz,SN + σz,cluster). By assuming η to be a constant and defined as functions of the redshift parameterized by six different expressions, we find that there exists no observable evidence for variations in the DD relation based on the collected data, since related statistical tests are well satisfied within the 1σ confidence level for most cases. Further, considering different values of Δz as constraints, we also find that the choice of Δz may play an important role in this model-independent test of the DD relation for the spherical sample of galaxy clusters.