Probing the Cosmic Distance Duality Relation with the Sunyaev-Zeldovich Effect, X-rays Observations and Supernovae Ia

The angular diameter distances toward galaxy clusters can be determined with measurements of the Sunyaev-Zel'dovich effect and X-ray surface brightness combined with the validity of the distance-duality relation, $D_L(z) (1 + z)^{2}/D_{A}(z) = 1$, where $D_L(z)$ and $D_A(z)$ are, respectively, the luminosity and angular diameter distances. This combination enables us to probe galaxy cluster physics or even to test the validity of the distance-duality relation itself. We explore these possibilities based on two different, but complementary approaches. Firstly, in order to constrain the possible galaxy cluster morphologies, the validity of the distance-duality relation (DD relation) is assumed in the $\Lambda$CDM framework (WMAP7). Secondly, by adopting a cosmological-model-independent test, we directly confront the angular diameters from galaxy clusters with two supernovae Ia (SNe Ia) subsamples (carefully chosen to coincide with the cluster positions). The influence of the different SNe Ia light-curve fitters in the previous analysis are also discussed. We assumed that $\eta$ is a function of the redshift parametrized by two different relations: $\eta(z) = 1 + \eta_{0}z$, and $\eta(z)=1 + \eta_{0}z/(1+z)$, where $\eta_0$ is a constant parameter quantifying the possible departure from the strict validity of the DD relation. The statistical analysis presented here provides new evidence that the true geometry of clusters is elliptical. We find that the two-light curve fitters (SALT2 and MLCS2K2) present a statistically significant conflict, and a joint analysis involving the different approaches suggests that clusters are endowed with an elliptical geometry as previously assumed.