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), DL=DA(1+z)2, where DL and DA are the luminosity and angular diameter distances, respectively. The data used correspond to 61 Type Ia Supernova luminosity distances and YSZE-YX measurements of 61 galaxy clusters obtained by the Planck mission and the deep XMM-Newton X-ray data, where YSZE is the integrated comptonization parameter obtained via Sunyaev-Zel'dovich effect observations and YX is the X-ray counterpart. More precisely, we use the YSZEDA 2/CXSZEYX scaling-relation and a deformed CDDR, such as DL/DA(1+z)2=η(z), to verify if η(z) is compatible with the unity. Two η(z) functions are used, namely, η(z)=1+η0 z and η(z)=1+η0 z /(1+z). We obtain that the CDDR validity (η0=0) is verified within 1.5σ c.l. for both η(z) functions.