Relativistic magnetised perturbations: magnetic pressure vs magnetic
  tension
  We study the linear evolution of magnetised cosmological perturbations in the
post-recombination epoch. Using full general relativity and adopting the ideal
magnetohydrodynamic approximation, we refine and extend the previous
treatments. More specifically, this is the first relativistic study that
accounts for the effects of the magnetic tension, in addition to those of the
field's pressure. Our solutions show that on sufficiently large scales, larger
than the (purely magnetic) Jeans length, the perturbations evolve essentially
unaffected by the magnetic presence. The magnetic pressure dominates on small
scales, where it forces the perturbations to oscillate and decay. Close to the
Jeans length, however, the field's tension takes over and leads to a weak
growth of the inhomogeneities. These solutions clearly demonstrate the opposing
action of the aforementioned two magnetic agents, namely of the field's
pressure and tension, on the linear evolution of cosmological density
perturbations.
