Gravitational Stability and Bulk Cosmology

TL;DR

This paper explores how bulk viscosity affects the stability of the early universe and the gravitational collapse of gas clouds, revealing conditions that suppress structure formation and influence collapse dynamics.

Contribution

It provides a detailed analysis of bulk viscosity effects on cosmological stability and collapse, introducing a critical viscosity threshold and identifying a viscous Jeans length.

Findings

Viscosity suppresses density contrast growth when exceeding a critical value.

Bulk viscosity can prevent sub-structure formation in collapsing gas clouds.

A viscous Jeans length determines the scale at which perturbations grow.

Abstract

We present a discussion of the effects induced by bulk viscosity either on the very early Universe stability and on the dynamics associated to the extreme gravitational collapse of a gas cloud. In both cases the viscosity coefficient is 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 the first case, matter filling the isotropic and homogeneous background is described by an ultra-relativistic equation of state. The analytic expression of the density contrast shows that its growth is suppressed forward in time as soon as $\zeta_0$ overcomes a critical value. On the other hand, in such a regime, the asymptotic approach to the initial singularity admits an unstable collapsing picture. In the second case, we investigate the top-down fragmentation process of an uniform and spherically symmetric gas cloud within the framework of a Newtonian approach, including the negative pressure contribution associated to the bulk viscous phenomenology. In the extreme regime toward the singularity, we show that the density contrast associated to an adiabatic-like behavior of the gas (which is identified by a particular range of the politropic index) acquire, for sufficiently large viscous contributions, a vanishing behavior which prevents the formation of sub-structures. Such a feature is not present in the isothermal-like collapse. We also emphasize that in the adiabatic-like case bulk viscosity is also responsible for the appearance of a threshold scale (equivalent to a Jeans length) beyond which perturbations begin to increase.