The Constraint of H0from Galaxy clusters and Hubble parameter data

Abstract

Using comoving distance $d_c$ and angular diameter distance $d_A$, 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 $d_c$ comes from Hubble data H(z) and is more reliable. Angular diameter distance $d_A$ 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 $z$; in high redshift case, we take variable substitution $y=1/(1+z)$, and expand the relation between luminosity distance and redshift about variable $y$ in order to reduce computational errors. Finally we get the more precise value of Hubble parameter $H_0=69.13\pm 0.24{\kern 1pt} km{\kern 1pt} \cdot {s^{ - 1}} \cdot Mp{c^{ - 1}}$, corresponding to 0.4\% uncertainty in $68.3\%$ confidence region, also deceleration factor $q_0=-0.57\pm0.04 $ and acceleration rate $j_0=1.28\pm0.33$, and their statistical values and probability graph. We compare the values of ${H_0}$, ${q_0}$, ${j_0}$ with those obtained from other observation data and model.