Galaxy cluster Sunyaev-Zel'dovich effect scaling-relation and type Ia supernova observations as a test for the cosmic distance duality relation

Abstract

In this paper, we propose a new test to the cosmic distance duality relation (CDDR), $D_L=D_A(1+z{)}^2$, where $D_L$ and $D_A$ are the luminosity and angular diameter distances, respectively. The data used correspond to 61 Type Ia Supernova luminosity distances and $Y_{SZE}-Y_X$ measurements of 61 galaxy clusters obtained by the {\it Planck} mission and the deep XMM-Newton X-ray data, where $Y_{SZE}$ is the integrated comptonization parameter obtained via Sunyaev-Zel'dovich effect observations and $Y_X$ is the X-ray counterpart. More precisely, we use the $Y_{SZE}{D}_A^2/C_{XSZE}{Y}_X$ scaling-relation and a deformed CDDR, such as $D_L/D_A(1+z{)}^2=\eta (z)$, to verify if $\eta (z)$ is compatible with the unity. Two $\eta (z)$ functions are used, namely, $\eta (z)=1+{\eta }_{0}z$ and $\eta (z)=1+{\eta }_{0}z/(1+z)$. { We obtain that the CDDR validity (${\eta }_0=0$) is verified within $\approx 1.5\sigma$ c.l. for both $\eta (z)$ functions.}.

7 pages, two figures, I table, Version accepted for publication in the JCAP