A Generalized Solution of Bianchi Type-V Models with Time-dependent $G$ and $\Lambda$

TL;DR

This paper derives exact solutions for Bianchi type-V cosmological models with time-varying G and Lambda, revealing different long-term behaviors and isotropization depending on parameter choices.

Contribution

It presents new exact solutions to Einstein's equations for anisotropic models with dynamic constants, including models with decreasing or increasing G and Lambda over time.

Findings

Models show Lambda decreasing and G increasing with time in one case.

Models become isotropic at late times under certain parameters.

Both G and Lambda can decrease while anisotropy increases in another model.

Abstract

We study the homogeneous but anisotropic Bianchi type-V cosmological model with time-dependent gravitational and cosmological "constants". Exact solutions of the Einstein field equations (EFEs) are presented in terms of adjustable parameters of quantum field theory in a spatially curved and expanding background. It has been found that the general solution of the average scale factor R as a function of time involved the hypergeometric function. Two cosmological models are obtained from the general solution of the hypergeometric function and the Emden-Fowler equation. The analysis of the models shows that for a particular choice of parameters in our first model, the cosmological "constant" decreases whereas the Newtonian gravitational "constant" increases with time, and for another choice of parameters, the opposite behaviour is observed. The models become isotropic at late times for all parameter choices of the first model. In the second model of the general solution, both the cosmological and gravitational "constants" decrease while the model becomes more anisotropic over time. The exact dynamical and kinematical quantities have been calculated analytically for each model.