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

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.}.