Constraining The Hubble Parameter Using Distance Modulus - Redshift Relation

Abstract

Using the relation between distance modulus $(m - M)$ and redshift $z$, deduced from Friedman- Robertson-Walker (FRW) metric and assuming different values of deceleration parameter $q_0$. We constrained the Hubble parameter $h$. The estimates of the Hubble parameters we obtained using the median values of the data obtained from NASA Extragalactic Database (NED), are: $h = 0.7\pm0.3$, for $q_0 = 0$, $h = 0.6\pm0.3$, for $q_0 = 1$ and $h = 0.8\pm0.3$ , for $q_0 = -1$. The corresponding age $\tau$ and size $R$ of the observable universe were also estimated as: $\tau = 15\pm1$ $ Gyr$, $R = (5\pm2) \times 10^3$ $Mpc$, $\tau = 18\pm1$ $Gyr$, $R=(6\pm2)\times 10^3$ $Mpc$ and $\tau=13\pm1$ $Gyr$, $R = (4 \pm 2)\times10^3$ $Mpc$ for $q_0 = 0$, $q_0 = 1$ and $q_0 = -1$ respectively.