Classical Bianchi type I cosmology in K-essence theory

TL;DR

This paper explores classical Bianchi type I cosmology within K-essence theory, deriving solutions for various matter contents and analyzing isotropization, with implications for understanding anisotropic universe evolution.

Contribution

It provides the first closed-form solutions for Bianchi type I models in K-essence theory with matter and cosmological constant, including isotropization analysis.

Findings

Closed-form solutions for non-stiff fluids without cosmological constant.

Isotropization can lead to constant or zero anisotropy ratios.

Qualitative analysis of the Friedmann-like equation in this context.

Abstract

We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid modeling the usual matter content and with cosmological constant. The classical solutions for any but the stiff fluid and without cosmological constant are found in closed form, using a time transformation. We also present the solution whith cosmological constant and some particular values of the barotropic parameter. We present the possible isotropization of the cosmological model, using the ratio between the anisotropic parameters and the volume of the universe and show that this tend to a constant or to zero for different cases. We include also a qualitative analysis of the analog of the Friedmann equation.