Testing the Distance-Duality Relation with Galaxy Clusters and Type Ia Supernovae

TL;DR

This study tests the distance-duality relation using galaxy clusters and Type Ia supernovae data, finding results that challenge the relation depending on the cluster geometry assumptions.

Contribution

It introduces a new model-independent test of the distance-duality relation using combined SNe Ia and galaxy cluster data with careful redshift matching.

Findings

Results marginally support the DD relation with elliptical cluster geometry.

Results strongly challenge the DD relation with spherical cluster geometry.

Constraints on the deviation parameter  suggest possible departures from the reciprocity relation.

Abstract

In this letter we propose a new and model-independent cosmological test for the distance-duality (DD) relation, \eta=D_{L}(z)(1+z)^{-2}/D_{A}(z)=1, where D_{L} and D_{A} are, respectively, the luminosity and angular diameter distances. For $D_L$ we consider two sub-samples of SNe type Ia taken from Constitution data (2009) whereas $D_A$ distances are provided by two samples of galaxy clusters compiled by De Fillipis et al. (2005) and Bonamente et al. (2006) by combining Sunyaev-Zeldovich effect (SZE) and X-ray surface brightness. The SNe Ia redshifts of each sub-sample were carefully chosen to coincide with the ones of the associated galaxy cluster sample (\Delta z<0.005) thereby allowing a direct test of DD relation. Since for very low redshifts, D_{A}(z) \approxeq D_{L}(z), we have tested the DD relation by assuming that $\eta$ is a function of the redshift parametrized by two different expressions: \eta(z) = 1 + \eta_{0}z and \eta(z) = 1 + \eta_{0}z/(1+z), where \eta_0 is a constant parameter quantifying a possible departure from the strict validity of the reciprocity relation (\eta_0=0). In the best scenario (linear parametrization) we obtain \eta_{0} = -0.28^{+ 0.44}_{- 0.44} (2\sigma$, statistical + systematic errors) for de Fillipis et al. sample (eliptical geometry), a result only marginally compatible with the DD relation. However, for Bonamente et al. sample (spherical geometry) the constraint is \eta_{0} = -0.42^{+ 0.34}_{- 0.34} (3\sigma$, statistical + systematic errors) which is clearly incompatible with the duality-distance relation.