  Gravitational instabilities in a magnetized Friedman - Robertson - Walker
(FRW) Universe, in which the magnetic field was assumed to be too weak to
destroy the isotropy of the model, are known and have been studied in the past.
Accordingly, it became evident that the external magnetic field disfavors the
perturbations' growth, suppressing the corresponding rate by an amount
proportional to its strength. However, the spatial isotropy of the FRW Universe
is not compatible with the presence of large-scale magnetic fields. Therefore,
in this article we use the general-relativistic (GR) version of the
(linearized) perturbed magnetohydrodynamic equations with and without
resistivity, to discuss a generalized Jeans criterion and the potential
formation of density condensations within a class of homogeneous and
anisotropically expanding, self-gravitating, magnetized fluids in curved
space-time. We find that, for a wide variety of anisotropic cosmological
models, gravito-magnetic instabilities can lead to sub-horizonal, magnetized
condensations. In the non-resistive case, the power spectrum of the unstable
cosmological perturbations suggests that most of the power is concentrated on
large scales (small k), very close to the horizon. On the other hand, in a
resistive medium, the critical wave-numbers so obtained, exhibit a delicate
dependence on resistivity, resulting in the reduction of the corresponding
Jeans lengths to smaller scales (well bellow the horizon) than the
non-resistive ones, while increasing the range of cosmological models which
admit such an instability.
