Cosmological perturbations on a magnetized Bianchi I background

Motivated by the isotropy of the CMB spectrum, all existing studies of magnetized cosmological perturbations employ FRW backgrounds. However, it is important to know the limits of this approximation and the effects one loses by neglecting the anisotropy of the background magnetic field. We develop a new treatment, which fully incorporates the anisotropic magnetic effects by allowing for a Bianchi I background universe. The anisotropy of the unperturbed model facilitates the closer study of the coupling between magnetism and geometry. The latter leads to a curvature stress, which accelerates positively curved perturbed regions and balances the effect of magnetic pressure gradients on matter condensations. We argue that the tension carried along the magnetic force lines is the reason behind these magneto-curvature effects. For a relatively weak field, we also compare with the results of the almost-FRW approach. We find that some of the effects identified by the FRW treatment are in fact direction-dependent, where the key direction is that of the background magnetic field vector. Nevertheless, the FRW-based approach to magnetized cosmological perturbations remains an accurate approximation, particularly on large scales, when one looks at the lowest-order magnetic impact on gravitational collapse. On small scales, however, the accuracy of the perturbed Friedmann framework may be compromised by extra shear effects.