An exact solution of the observable universe in Bianchi V space-time

TL;DR

This paper presents an exact solution for an observable universe model within Bianchi V space-time, incorporating a cosmological constant, and validates it using supernova and Hubble data, revealing a transitioning universe in accelerated expansion.

Contribution

It provides an exact Bianchi V universe model with a cosmological constant and fits it to observational data, showing a transition from deceleration to acceleration.

Findings

Current Hubble constant estimated from data.

Deceleration parameter indicates a transition from positive to negative.

Universe's age and jerk parameter align with Planck and WMAP results.

Abstract

In this paper we investigate an observable universe in Bianchi type V space-time by taking into account the cosmological constant as the source of energy. We have performed a $\chi^{2}$ test to obtain the best fit values of the model parameters of the universe in the derived model. We have used two types of data sets, viz: i) 31 values of the Hubble parameter and ii) the 1048 Phanteon data set of various supernovae distance moduli and apparent magnitudes. From both the data sets, we have estimated the current values of the Hubble constant, density parameters $(\Omega_{m})_{0}$ and $(\Omega_{\Lambda})_{0}$. The present value of deceleration parameter of the universe in derived model is obtained as $q_{0} = 0.59^{+0.04}_{-0.03}$ and $0.59^{+0.02}_{-0.03}$ in accordance with $H(z)$ and Pantheon data respectively. Also we observe that there is a signature flipping in the sign of deceleration parameter from positive to negative and transition red-shift exists. Thus, the universe in derived model represents a transitioning universe which is in accelerated phase of expansion at present epoch. We have estimated the current age of the universe $(t_{0})$ and present value of jerk parameter $(j_{0})$. Our obtained values of $t_{0}$ and $j_{0}$ are in good agreement with its values estimated by Plank collaborations and WMAP observations.