Nonlinear spinor field in Bianchi type-I Universe filled with viscous fluid: numerical solutions

TL;DR

This paper investigates the evolution of a Bianchi type-I universe filled with viscous fluid and nonlinear spinor fields, deriving and numerically solving the coupled equations to understand their dynamics.

Contribution

It introduces a self-consistent numerical approach to solve the coupled spinor and gravitational field equations with viscous fluid in Bianchi type-I spacetime.

Findings

Numerical solutions for the universe's volume scale and fluid energy are obtained.

The model demonstrates the influence of nonlinear spinor fields on cosmological evolution.

Abstract

We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be $\lambda F$, with $\lambda$ being a self-coupling constant and $F$ being a function of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of $\tau$, where $\tau$ is the volume scale of BI universe. System of equations for $\tau$ and $\ve$, where $\ve$ is the energy of the viscous fluid, is deduced. This system is solved numerically for some special cases.