Dynamical systems approach to magnetized cosmological perturbations - art.no. 124007

Assuming a large-scale homogeneous magnetic field, we follow the covariant and gauge-invariant approach used by Tsagas and Barrow to describe the evol ution of density and magnetic field inhomogeneities and curvature perturbat ions in a matter-radiation universe. We use a two parameter approximation s cheme to linearize their exact non-linear general-relativistic equations fo r magneto-hydrodynamic evolution. Using a two-fluid approach we set up the governing equations as a fourth order autonomous dynamical system. Analysis of the equilibrium points for the radiation dominated era lead to solution s similar to the super-horizon modes found analytically by Tsagas and Maart ens. We find that a study of the dynamical system in the dust-dominated era leads naturally to a magnetic critical length scale closely related to the Jeans length. Depending on the size of wavelengths relative to this scale, these solutions show three distinct behaviors: large-scale stable growing modes, intermediate decaying modes, and small-scale damped oscillatory solu tions.