The constraint of H0 from galaxy clusters and Hubble parameter data

Abstract

Using comoving distance [Formula: see text] and angular diameter distance [Formula: see text], we recalculate parameters describing kinematical state of the universe, still combining the kinematical model of universe but not relying on dynamical equations for gravity. Comoving distance [Formula: see text] comes from Hubble data [Formula: see text] and is more reliable. Angular diameter distance [Formula: see text] comes from SZE (Sunyaev–Zel’dovich Effect) and X-ray data, and needs calibration. In low redshift case, we use expansion of relation between luminosity distance and redshift about redshift [Formula: see text]; in high redshift case, we take variable substitution [Formula: see text], and expand the relation between luminosity distance and redshift about variable [Formula: see text] in order to reduce computational errors. Finally, we get the more precise value of Hubble parameter [Formula: see text] km ⋅ s[Formula: see text], corresponding to [Formula: see text] uncertainty in [Formula: see text] confidence region, also deceleration factor [Formula: see text] and acceleration rate [Formula: see text], and their statistical values and probability graph. We compare the values of [Formula: see text], [Formula: see text] and [Formula: see text] with those obtained from other observation data and model.