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

TL;DR

This study tests the cosmic distance duality relation using galaxy cluster gas mass fractions and supernova data, finding consistency with the relation for one dataset but conflict for another, indicating possible model or data assumptions issues.

Contribution

It introduces a model-independent test of the cosmic distance duality relation combining X-ray gas mass fraction and supernova data, highlighting dataset-dependent results.

Findings

La Roque et al. sample agrees with the duality relation

Ettori et al. sample shows significant conflict

Results depend on cluster data assumptions

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.