A cosmological model with time dependent $\Lambda$, $G$ and viscous fluid in General Relativity

TL;DR

This paper explores a Bianchi type-V cosmological model with viscous fluid, where both the cosmological constant and gravitational constant vary over time, showing a universe evolving from deceleration to acceleration consistent with observations.

Contribution

It introduces a novel cosmological model with time-dependent $\Lambda$ and $G$ in a viscous fluid context, solved numerically using the Runge-Kutta method.

Findings

Universe starts with negative $\Lambda$, matter-dominated, decelerated

Transitions to $\Lambda$-dominated, accelerated expansion

Model aligns with current cosmological observations

Abstract

In this paper, we investigate Bianchi type$-V$ cosmological models with bulk viscous fluid and time varying cosmological $\Lambda$ and Newtonian $G$ parameters. The Einstein's field equations have been transformed into a coupling non-linear, first-order differential equations, and the fourth-order Runge-Kutta method of numerical integration has been used to integrate the differential equations with appropriate initial conditions consistent with current cosmological observations. We show that the model describes a universe that starts off with a negative cosmological term, as well as a matter-dominated and decelerated early epoch that, eventually becomes $\Lambda$-dominated and expanding with acceleration, in concordance with current observations.