Constraints on the Hubble Parameter from galaxy clusters and the Validity of the Cosmic Distance Duality Relation

Abstract

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 $H_0^{\ast }=H_0/{\eta }^2$. 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 parameterizations, we obtain constraints on $H_0$ regardless of the validity of the DD relation. For the linear and non linear $\eta (z)$ functions, we obtain $H_0=75_{-7}^{+7}$ km/s/Mpc and $H_0=75_{-7}^{+10}$ km/s/Mpc, respectively (without systematic erros). 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.

10 pages, 5 figures, IJMPD (in Press)

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