The Hubble constant from galaxy cluster scaling-relation and SNe Ia observations: a consistency test

Abstract

In this paper, we propose a self-consistent test for a Hubble constant estimate using galaxy cluster and type Ia supernovae (SNe Ia) observations. The approach consists, in a first step, of obtaining the observational value of the galaxy cluster scaling-relation Y_{SZE}D_{A}^{2}/C_{XSZ}Y_X = C by combining the X-Ray and SZ observations of galaxy clusters at low redshifts (z < 0.1) from the first Planck mission all-sky data set (0.044 le z le 0.444), along with SNe Ia observations and making use of the cosmic distance duality relation validity. Then, by considering a flat Lambda CDM model for D_A, the constant C from the first step and the Planck prior on Omega _M parameter, we obtain H_0 by using the galaxy cluster data with z>0.1. As a result, we obtain { H_0=73.014^{+7.435}_{-6.688}} km/s/Mpc, in full agreement with the latest results from HST + SH0ES team. We also compare our method with that one where the C parameter is obtained from hydrodynamical simulations of massive galaxy clusters.