Study of the Quasi-isotropic Solution near the Cosmological Singularity in Presence of Bulk-Viscosity

TL;DR

This paper investigates how bulk viscosity affects the behavior of a quasi-isotropic universe near the cosmological singularity, identifying specific conditions where viscosity influences but does not dominate the dynamics.

Contribution

It introduces a detailed analysis of bulk viscosity effects with a specific power-law dependence, extending the quasi-isotropic solution framework to include viscous fluids near singularities.

Findings

Viscosity influences the singularity physics without dominating the universe's dynamics.

Power-law solutions exist only within a restricted domain of the viscosity parameter.

The study clarifies the role of bulk viscosity in early universe models.

Abstract

We analyze the dynamical behavior of a quasi-isotropic Universe in the presence of a cosmological fluid endowed with bulk viscosity. We express the viscosity coefficient as a power-law of the fluid energy density: $\zeta=\zeta_0\epsilon^{s}$. Then we fix $s=1/2$ as the only case in which viscosity plays a significant role in the singularity physics but does not dominate the Universe dynamics (as requested by its microscopic perturbative origin). The parameter $\zeta_0$ is left free to define the intensity of the viscous effects. Following the spirit of the work by E.M. Lifshitz and I.M. Khalatnikov on the quasi-isotropic solution, we analyze both Einstein and hydrodynamic equations up to first and second order in time. As a result, we get a power-law solution existing only in correspondence to a restricted domain of $\zeta_0$.