CONSTRAINTS ON THE HUBBLE PARAMETER FROM GALAXY CLUSTERS AND THE VALIDITY OF THE COSMIC DISTANCE DUALITY RELATION

Abstract

Constraints on the Hubble parameter, H0, via X-ray surface brightness and Sunyaev–Zel'dovich effect (SZE) observations of the galaxy clusters depend on the validity of the cosmic distance duality relation (DD relation), η = DL(z)(1+z)-2/DA(z) = 1, where DL and DA are the luminosity distance and angular diameter distance (ADD), respectively. In this work, we argue that if the DD relation does not hold, the X-ray plus SZE technique furnishes a [Formula: see text]. We use 25 ADD of galaxy clusters to obtain simultaneous constraints on H0 and possible violation of the DD relation in a flat ΛCDM model. Such a violation is parametrized by two functions: η(z) = 1 + η0z and η(z) = 1 + η0z/(1+z), where η0 is a constant parameter quantifying possible departures from the strict validity. Finally, by marginalizing on the η0 in both parametrizations, we obtain constraints on H0 regardless of the validity of the DD relation. For the linear and nonlinear η(z) functions, we obtain [Formula: see text] km/s/Mpc and [Formula: see text] km/s/Mpc, respectively (without systematic errors). Our results support recent H0 measurements by using X-ray and SZE observations of galaxy clusters which have taken the distance duality as valid.