On the Role of Viscosity in Early Cosmology

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 ρ via a power-law of the form ζ = ζ0ρ s (where ζ0, 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 ζ0. 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. 1 The Quasi-Isotropic model In 1963, E.M. Lifshitz and I.M. Khalatnikov [1] proposed the so-called quasi-isotropic solution. This model is based on the idea that a Taylor expansion, in time, of the 3-metric can be addressed. In this approach, the Friedmann solution becomes a particular case of a larger class of solutions, existing only for space filled with matter. In fact, for an ultra-relativistic perfect fluid (p = ρ/3, ρ being the energy density of the fluid), the spatial metric assumes the form γαβ ∼ aαβ(x) t, asymptotically towards the singularity as t → 0. As a function of time, the 3-metric is expandable in powers of t. The quasi-isotropic solution is formulated in a synchronous system (i.e., g0α = 0, g00 = −1), with a line element of the form ds = −dt + γαβ(t, x)dxdx , γαβ = t aαβ + t bαβ + ... , (1) and a is defined as aaβγ = δ α γ , moreover b α β = a bγβ. Using the extrinsic curvature