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

TL;DR

This study investigates how the validity of the cosmic distance duality relation affects measurements of the Hubble constant using galaxy cluster observations, finding results consistent with recent measurements assuming the relation holds.

Contribution

It provides a method to constrain the Hubble constant independently of the DD relation's validity by marginalizing over possible violations.

Findings

H_0 estimated as 75^{+7}_{-7} km/s/Mpc assuming DD validity.

H_0 estimated as 75^{+10}_{-7} km/s/Mpc allowing DD violation.

Results support previous H_0 measurements based on galaxy clusters.

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 $H^{*}_{0}=H_{0}/\eta^{2}$. 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 $H_{0}= 75^{+ 10}_{-7}$ 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.