On the Role of Viscosity in Early Cosmology

TL;DR

This paper investigates how bulk viscosity affects the stability of the very early Universe, analyzing density contrast behavior near the singularity with a focus on power-law viscosity models.

Contribution

It introduces a detailed analysis of viscosity effects on early cosmological stability using quasi-isotropic models and explores the conditions for power-law solutions near the singularity.

Findings

Power-law solutions exist only within specific viscosity parameter ranges.

The isotropic FRW model shows an unstable approach to the initial singularity.

Viscosity influences the stability and behavior of density perturbations.

Abstract

We present a discussion of the effects induced by bulk viscosity on the very early Universe stability. The viscosity coefficient is assumed to be related to the energy density $\rho$ via a power-law of the form $\zeta=\zeta_0 \rho^s$ (where $\zeta_0, s=const.$) and the behavior of the density contrast in analyzed. In particular, we study both Einstein and hydrodynamic equations up to first and second order in time in the so-called quasi-isotropic collapsing picture near the cosmological singularity. As a result, we get a power-law solution existing only in correspondence to a restricted domain of $\zeta_0$. The particular case of pure isotropic FRW dynamics is then analyzed and we show how the asymptotic approach to the initial singularity admits an unstable collapsing picture.