Gravitational instability of the primordial plasma: anisotropic evolution of structure seeds

We study how the presence of a background magnetic field, of intensity compatible with current observation constraints, affects the linear evolution of cosmological density perturbations at scales below the Hubble radius. The magnetic field provides an additional pressure that can prevent the growth of a given perturbation; however, the magnetic pressure is confined only to the plane orthogonal the field. As a result, the "Jeans length" of the system not only depends on the wavelength of the fluctuation but also on its direction, and the perturbative evolution is anisotropic. We derive this result analytically and back it up with direct numerical integration of the relevant ideal magnetohydrodynamics equations during the matter-dominated era. Before recombination, the kinetic pressure dominates and the perturbations evolve in the standard way, whereas after that time magnetic pressure dominates and we observe the anisotropic evolution. We quantify this effect by estimating the eccentricity $\epsilon$ of a Gaussian perturbation in the coordinate space that was spherically symmetric at recombination. For perturbations at the sub-galactic scale, we find that $\epsilon = 0.7$ at $z=10$ taking the background magnetic field of order $10^{-9}$ gauss.