Similarity dark energy models in Bianchi type - I space-time

TL;DR

This paper explores new inhomogeneous solutions in anisotropic dark energy models within Bianchi type-I space-time, analyzing their symmetry properties, solutions, and anisotropic behaviors using Lie symmetry methods.

Contribution

It introduces novel similarity solutions for anisotropic dark energy in Bianchi type-I space-time and applies Lie symmetry analysis to solve the Einstein field equations.

Findings

Derived new inhomogeneous solutions with anisotropic dark energy

Analyzed the symmetry properties and reduced PDEs to ODEs

Examined the anisotropy behavior and geometrical features of the models

Abstract

We investigate some new similarity inhomogeneous solutions of anisotropic dark energy and perfect fluid in Bianchi type-I space-time. Three different equation of state parameters along the spatial directions are introduced to quantify the deviation of pressure from isotropy. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system of one-dimensional subalgebras. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analyzed. We solve the Einstein field equations, described by a system of non-linear partial differential equations (NLPDEs), by using the Lie point symmetry analysis method. The geometrical and kinematical features of the models and the behavior of the anisotropy of dark energy, are examined in detail.