Magnetized cosmological perturbations in the post-recombination era

Abstract

We study inhomogeneous magnetised cosmologies through the post-recombination era in the framework of Newtonian gravity and the ideal-magnetohydrodynamic limit. The nonlinear kinematic and dynamic equations are derived and linearised around the Newtonian counterpart of the Einstein-de Sitter universe. This allows for a direct comparison with the earlier relativistic treatments of the issue. Focusing on the evolution of linear density perturbations, we provide new analytic solutions which include the effects of the magnetic pressure as well as those of the field's tension. We confirm that the pressure of field inhibits the growth of density distortions and can induce a purely magnetic Jeans length. On scales larger than the aforementioned characteristic length the inhomogeneities grow, though slower than in non-magnetised universes. Wavelengths smaller than the magnetic Jeans length typically oscillate with decreasing amplitude. We also identify a narrow range of scales, just below the Jeans length, where the perturbations exhibit a slower power-law decay. In all cases, the effect of the field is proportional to its strength and increases as we move to progressively smaller lengths.

Relativistic magnetised perturbations: magnetic pressure versus magnetic tension

“…The linear contribution of the magnetic tension, on the other hand, is two-fold. There are pure-tension stresses, similar but not identical to those identified in the Newtonian study of [15], and a purely relativistic magneto-curvature stress triggered by the non-Euclidean geometry of the host space. Both of these tension stresses reflect the elasticity of the magnetic forcelines and their generic tendency to react against any agent (physical or geometrical) that distorts them from equilibrium [18]-[20].We analyse the role of the B-field in a step-by-step approach, accounting for the effects of the magnetic pressure first, before gradually incorporating those of the field's tension.…”

“…The magnetic contribution to the linear equations comes always through terms of order B 2 (see expressions(15)-(17)), which ensures the perturbative consistency of the adopted linearisation scheme.…”

“…Then, setting w = 0 and c 2 a =B 2 /ρ ≪ 1, the comoving 3divergences of Eqs. (15), (16) and (17) lead to the linear propagation formulaė…”

“…The effects of the magnetic tension, that is of the negative pressure exerted along the field lines themselves, have never been accounted for. The only exception has been a recent Newtonian study, where the role of the magnetic tension on the linear evolution of density inhomogeneities in the post-recombination universe was investigated [15]. That work indicated that the aforementioned two magnetic agents may have opposing action, but the results were not conclusive.Here, we provide the first (to the best of our knowledge) fully relativistic study of magnetised density perturbations that incorporates the effects of the field's tension, in addition to those of its (positive) pressure.…”

“…A closer look into the study of[15] reveals that solutions (42) and (43) reside in the Newtonian equations as well, although not as distinct special cases, which is probably the reason they were not identified there.…”