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

Abstract

In this paper we discuss a new cosmological model-independent test for the cosmic distance duality relation (CDDR), $\eta =D_L(L)(1+z{)}^{-2}/D_A(z)=1$, where $D_A(z)$ and $D_L(z)$ are the angular and luminosity distances, respectively. Using the general expression for X-ray gas mass fraction ($f_{gas}$) of galaxy clusters, $f_{gas}\propto D_L{D_A}^{1/2}$, we show that $f_{gas}$ observations jointly with type Ia supernovae (SNe Ia) data furnish a validity test for the CDDR. To perform our analysis we use 38 $f_{gas}$ measurements recently studied by two groups considering different assumptions to describe the clusters (La Roque {\it{et al.}} 2006 and Ettori {\it{et al.}} 2009) and two subsamples of SNe Ia distance luminosity extracted from the Union2 compilation. In our test we consider the $\eta$ parameter as a function of the redshift parameterized by two different functional forms. It is found that the La Roque {\it{et al.}} (2006) sample is in perfect agreement with the duality relation ($\eta =1$) whereas the Ettori {\it{et al.}} (2009) sample presents a significant conflict.

Comments: 5 pages, 2 figures, 1 table, Letter to MNRAS (in press)