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

Constraints on the Hubble parameter, H-0, 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), eta = D-L(z)(1 + z)(-2)/D-A(z) = 1, where D-L and D-A 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 H*(0) = H-0/eta(2). We use 25 ADD of galaxy clusters to obtain simultaneous constraints on H-0 and possible violation of the DD relation in a flat Lambda CDM model. Such a violation is parametrized by two functions: eta(z) = 1 + eta(0)z and eta(z) = 1+eta(0)z/(1+ z), where eta(0) is a constant parameter quantifying possible departures from the strict validity. Finally, by marginalizing on the eta(0) in both parametrizations, we obtain constraints on H-0 regardless of the validity of the DD relation. For the linear and nonlinear eta(z) functions, we obtain H-0 = 75(-7)(+7) km/s/Mpc and H-0 = 75(-7)(+10) km/s/Mpc, respectively (without systematic errors). Our results support recent H-0 measurements by using X-ray and SZE observations of galaxy clusters which have taken the distance duality as valid.