Gradient expansion, curvature perturbations and magnetized plasmas
  The properties of magnetized plasmas are always investigated under the
hypothesis that the relativistic inhomogeneities stemming from the fluid
sources and from the geometry itself are sufficiently small to allow for a
perturbative description prior to photon decoupling. The latter assumption is
hereby relaxed and pre-decoupling plasmas are described within a suitable
expansion where the inhomogeneities are treated to a given order in the spatial
gradients. It is argued that the (general relativistic) gradient expansion
shares the same features of the drift approximation, customarily employed in
the description of cold plasmas, so that the two schemes are physically
complementary in the large-scale limit and for the low-frequency branch of the
spectrum of plasma modes. The two-fluid description, as well as the
magnetohydrodynamical reduction, are derived and studied in the presence of the
spatial gradients of the geometry. Various solutions of the coupled system of
evolution equations in the anti-Newtonian regime and in the quasi-isotropic
approximation are presented. The relation of this analysis to the so-called
separate Universe paradigm is outlined. The evolution of the magnetized
curvature perturbations in the nonlinear regime is addressed for the magnetized
adiabatic mode in the plasma frame.
