Bulk Viscosity Effects on the Early Universe Stability

Abstract

We present a discussion of the effects induced by the bulk viscosity on the very early Universe stability. The matter filling the cosmological (isotropic and homogeneous) background is described by a viscous fluid having an ultrarelativistic equation of state and whose viscosity coefficient is related to the energy density via a power-law of the form $\zeta=\zeta_0 \rho^\nu$. The analytic expression of the density contrast (obtained for $\nu=1/2$) shows that, for small values of the constant $\zeta_0$, its behavior is not significantly different from the non-viscous one derived by E.M. Lifshitz. But as soon as $\zeta_0$ overcomes a critical value, the growth of the density contrast is suppressed forward in time by the viscosity and the stability of the Universe is favored in the expanding picture. On the other hand, in such a regime, the asymptotic approach to the initial singularity (taken at $t=0$) is deeply modified by the apparency of significant viscosity in the primordial thermal bath i.e. the isotropic and homogeneous Universe admits an unstable collapsing picture. In our model this feature regards also scalar perturbations while in the non-viscous case it appears only for tensor modes.