Anisotropic background for two fluids: matter and holographic dark energy

TL;DR

This paper presents an exact solution for a Bianchi type-I universe with matter and holographic dark energy, showing a transition from early deceleration to current acceleration, consistent with observations.

Contribution

It introduces a hyperbolic scale factor in an anisotropic universe model with two fluids, providing new exact solutions and analyzing their physical implications.

Findings

Universe transitions from deceleration to acceleration

Model aligns with recent astronomical data

Anisotropic parameters are physically consistent

Abstract

We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time with two fluids as the content of the Universe: matter and holographic dark energy in the framework of general relativity. To get the exact solutions of Einstein's field equations, we choose the scale factor as a hyperbolic function, specifically, $a\left( t\right) =\sinh ^{\frac{1}{n}}\left( \gamma t\right) $, where $\gamma $ and $n>0$ are arbitrary constants, which gives us a time-dependent deceleration parameter. Then we study our cosmological model under the conditions of the parameters as: $\gamma $ fixed and $n>1$. Our cosmological solutions led to an early deceleration phase followed by the current observed acceleration phase. Further, the anisotropic parameter and some other physical parameters are discussed. We conclude that our cosmological model is consistent with the results of recent astronomical observations.