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.
