On the influence of viscosity on the anisotropic dynamics of cosmological perturbations in the presence of a magnetic field

We analyse the influence that viscous effects can induce on the evolution of primordial perturbations to the isotropic universe in the presence of a weak uniform magnetic field. Previous analyses have shown that the presence of the magnetic field induces an intrinsic anisotropy in the perturbations dynamics, essentially because of the anisotropic character of the perturbed magnetic pressure. This anisotropic effect is of order unity in the perturbation amplitude, although it remains small in the linear theory when the density constraints are considered. The aim of this study is to determine the impact of viscosity, surely present in the early universe, on the growth of the perturbation anisotropy. The main merit of this study consists of demonstrating that a tiny overlapping exists in the parameter space to deal simultaneously with anisotropic features due to the magnetic field and the viscous damping of such density fluctuation. Actually, we demonstrate that the viscosity affects the value of the anisotropy, by smoothing the growing rate of the instability only when structure smaller than about 5000 solar masses are concerned. This result allows us to guarantee that the intrinsic anisotropy of the magnetized universe perturbations is not affected by the viscosity due to friction among inhomogeneous layers or compressive-like effects, and therefore, they remain good candidates for being seeds for filament formation across the universe.