Testing the cosmic distance duality with X‐ray gas mass fraction and supernovae data

ABSTRACT In this Letter, we discuss a new cosmological‐model‐independent test for the cosmic distance duality relation (CDDR), η=DL(L)(1 +z)−2/DA(z) = 1, where DA(z) and DL(z) are the angular diameter and luminosity distances, respectively. Using the general expression for X‐ray gas mass fraction (fgas) of galaxy clusters, fgas∝DLDA1/2, we show that fgas observations jointly with Type Ia supernovae (SNe Ia) data furnish a validity test for the CDDR. To perform our analysis, we use 38 fgas measurements recently studied by two groups considering different assumptions to describe the clusters and two subsamples of SNe Ia distance luminosity extracted from the Union2 compilation. In our test, we consider the η parameter as a function of the redshift parametrized by two different functional forms. It is found that the La Roque et al. sample is in perfect agreement with the duality relation (η= 1), whereas the Ettori et al. sample presents a significant conflict.