Constraining The Hubble Parameter Using Distance Modulus - Redshift Relation

TL;DR

This paper uses the distance modulus-redshift relation derived from FRW metric to constrain the Hubble parameter and estimate the universe's age and size under different deceleration parameters.

Contribution

It provides new estimates of the Hubble parameter, universe age, and size based on observational data and different deceleration parameters, using a straightforward analytical approach.

Findings

Hubble parameter estimates: 0.7±0.3, 0.6±0.3, 0.8±0.3 for q0=0, 1, -1 respectively.

Estimated universe ages: 15±1 Gyr, 18±1 Gyr, 13±1 Gyr for q0=0, 1, -1 respectively.

Estimated universe sizes: (5±2)×10^3 Mpc, (6±2)×10^3 Mpc, (4±2)×10^3 Mpc for q0=0, 1, -1 respectively.

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.