Dynamical Systems Approach to Magnetised Cosmological Perturbations

TL;DR

This paper models the evolution of cosmological perturbations in a magnetized universe using a dynamical systems approach, revealing different behaviors depending on wavelength relative to a critical scale.

Contribution

It introduces a dynamical systems framework to analyze magnetized cosmological perturbations, extending previous covariant methods with a new approximation scheme.

Findings

Identifies a magnetic critical length scale related to the Jeans Length.

Finds stable growing modes on large scales.

Discovers damped oscillatory solutions on small scales.

Abstract

Assuming a large-scale homogeneous magnetic field, we follow the covariant and gauge-invariant approach used by Tsagas and Barrow to describe the evolution of density and magnetic field inhomogeneities and curvature perturbations in a matter-radiation universe. We use a two parameter approximation scheme to linearize their exact non-linear general-relativistic equations for 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 solutions similar to the super-horizon modes found analytically by Tsagas and Maartens. 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 behaviours: large-scale stable growing modes, intermediate decaying modes, and small-scale damped oscillatory solutions.