L.R.S. Bianchi type II Stiff Fluid cosmological model with Decaying Vacuum Energy Density $\Lambda$ in general relativity

TL;DR

This paper investigates a Bianchi type II cosmological model with stiff fluid and decaying vacuum energy, showing its consistency with observational data and describing an accelerating, shearing universe.

Contribution

It introduces a new deterministic Bianchi type II model with a specific metric potential relation and analyzes its physical and observational implications.

Findings

Vacuum energy density $\\Lambda$ is positive and proportional to $1/t^2$.

Model's parameters align with WMAP observations.

Predicted jerk parameter matches some supernova and galaxy data.

Abstract

Locally rotationally symmetric (L.R.S.) Bianchi type II stiff fluid cosmological model is investigated. To get the deterministic model of the universe, we have assumed a condition $A=B^{m}$ between metric potentials $A,~B$ where $n$ is the constant. It is shown that the vacuum energy density $\Lambda$ is positive and proportional to $\frac{1}{t^{2}}$. The values of deceleration parameter $q$, matter-energy density $\Omega_{m}$ and dark-energy density $\Omega_{\Lambda}$ are found to be in good agreement with the values obtain from 5-years WMAP observations. the predicted value of the jerk parameter agrees with the SNLS SNIa and X-ray galaxy cluster distance data but does not with the SNIa gold sample data. In general, the model represent accelerating, shearing and non-rotating universe.The physical and geometrical behavior of these models are also discussed.