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, \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.
