Dirac Spinor in Bianchi-I Universe with Time Dependent Gravitational and Cosmological Constants

TL;DR

This paper investigates the dynamics of a nonlinear spinor field coupled with Bianchi I universe models featuring time-dependent gravitational and cosmological constants, analyzing initial conditions, asymptotic behavior, and isotropization.

Contribution

It introduces a self-consistent model of nonlinear spinor and Bianchi I gravitational fields with variable $G$ and $mbda$, exploring their evolution and isotropization.

Findings

Behavior of spinor and metric functions at initial and late times

Expression for $G$ as a function of the volume element $ au$

Role of perfect fluid in early universe and isotropization process

Abstract

Self-consistent system of nonlinear spinor field and Bianchi I (BI) gravitational one with time dependent gravitational constant ($G$) and cosmological constant ($\Lambda$) has been studied. The initial and the asymptotic behaviors of the field functions and the metric one have been thoroughly investigated. Given $\Lambda = \Lambda_0/\tau^2$, with $\tau = \sqrt{-g}$, $G$ has been estimated as a function of $\tau$. The role of perfect fluid at the initial state of expansion and asymptotical isotropization process of the initailly anisotropic universe has been elucidated.