LAUSR

An important result from self-similar models that describe the process of galaxy cluster formation is the simple scaling relation $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X= C$. In this ratio, $Y_{SZE}$ is the integrated Sunyaev-Zel'dovich effect flux of a cluster, its X-ray counterpart is $Y_X$, $C_{XSZE}$ and $C$ are constants and $D_A$ is the angular diameter distance to the cluster. In this paper, we consider the cosmic distance duality relation validity jointly with type Ia supernovae observations plus $61$ $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X$ measurements as reported by the Planck Collaboration to explore if this relation is constant in the redshift range considered ($z<0.5$). No one specific cosmological model is used. As basic result, although the data sets are compatible with no redshift evolution within 2$\sigma$ c.l., a Bayesian analysis indicates that other $C(z)$ functions analyzed in this work cannot be discarded. It is worth to stress that the observational determination of an universal $C(z)$ function turns the $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X$ ratio in an useful cosmological tool to determine cosmological parameters. Moreover, the approach proposed here can also be used as a cross-check for those scaling relation calibration methods that use weak-lensing analyses.