Bianchi type I universe with viscous fluid: A qualitative analysis

TL;DR

This paper investigates how viscosity and the cosmological constant influence the evolution of a Bianchi type-I universe, revealing conditions for expansion, oscillation, and singularity avoidance through analytical and numerical methods.

Contribution

It provides a detailed analysis of viscous effects on Bianchi type-I cosmologies with a cosmological constant, highlighting new oscillatory behaviors induced by viscosity.

Findings

Viscosity and $\\Lambda$ significantly affect solution behavior.

Negative $\\Lambda$ leads to perpetual expansion.

Positive $\\Lambda$ can produce oscillatory, singularity-free solutions.

Abstract

The nature of cosmological solutions for a homogeneous, anisotropic Universe given by a Bianchi type-I (BI) model in the presence of a Cosmological constant $\Lambda$ is investigated by taking into account dissipative process due to viscosity. The system in question is thoroughly studied both analytically and numerically. It is shown the viscosity, as well as the $\Lambda$ term exhibit essential influence on the character of the solutions. In particular a negative $\Lambda$ gives rise to an ever-expanding Universe, whereas, a suitable choice of initial conditions plus a positive $\Lambda$ can result in a singularity-free oscillatory mode of expansion. For some special cases it is possible to obtain oscillations in the exponential mode of expansion of the BI model even with a negative $\Lambda$, where oscillations arise by virtue of viscosity.