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

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: $\zeta ={\zeta }_0{ϵ}^s$. Then we fix $s=1\mathrm{/}2$ 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 ${\zeta }_0$.