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

In this letter we propose a new and model-independent cosmological test for the distance-duality (DD) relation, η=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 (Δz<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 $η$ is a function of the redshift parametrized by two different expressions: η(z) = 1 + η_{0}z and η(z) = 1 + η_{0}z/(1+z), where η_0 is a constant parameter quantifying a possible departure from the strict validity of the reciprocity relation (η_0=0). In the best scenario (linear parametrization) we obtain η_{0} = -0.28^{+ 0.44}_{- 0.44} (2σ$, statistical + systematic errors) for de Fillipis et al. sample (eliptical geometry), a result only marginally compatible with the DD relation. However, for Bonamente et al. sample (spherical geometry) the constraint is η_{0} = -0.42^{+ 0.34}_{- 0.34} (3σ$, statistical + systematic errors) which is clearly incompatible with the duality-distance relation.