Qualitative analysis of viscous cosmology

TL;DR

This paper investigates how higher-order viscosity effects influence the evolution of a homogeneous, isotropic universe, revealing complex behaviors like bouncing and cyclic scenarios through dynamical system analysis.

Contribution

It introduces a second-order viscosity correction into cosmological models and analyzes its impact on universe dynamics using phase diagrams and bifurcation analysis.

Findings

Viscous effects can induce bouncing and cyclic universe scenarios.

Bifurcations lead to changes in stability and universe evolution.

Analytical equilibrium points depend on model parameters.

Abstract

We analyze the effect of higher order viscosity corrections in a spatially homogeneous and isotropic universe. The viscous effects are modeled by introducing a second-order term to the energy density in the equation of state and on the expansion factor. An autonomous dynamical system is then constructed to study the qualitative behavior of the energy density and expansion factor, employing the Raychaudhuri equation and the conservation of energy. We obtain the analytical expressions for the equilibrium points in terms of the model parameters, presenting several phase diagrams. The analysis of these diagrams reveals the presence of bifurcations, which manifest as changes in stability and qualitative behavior. Those changes lead to different configurations for the universe, such as bouncing, rebouncing and cyclic scenarios.