Generation of density perturbations by primordial magnetic fields

We study the generation and evolution of density perturbations and peculiar velocities due to primordial magnetic fields. We assume that a random magnetic field was present before recombination and follow the field's effect on the baryon fluid starting at recombination. We find that magnetic fields generate growing density perturbations on length scales larger than the magnetic Jeans length, λ_B, and damped oscillations for scales smaller than λ_B. For small wavenumbers k (large length scales), we find that the magnetic field-induced density power spectrum generally scales as k⁴. We derive the magnetic Jeans length explicitly by including the back-reaction of the velocity field onto the magnetic field and by decomposing the magnetic field into a force-free background field and perturbations about it. Depending on the strength of the magnetic field and the ultraviolet cutoff of its spectrum, structure can be generated on small or intermediate scales early in the history of the universe. For a present rms magnetic field of 10^-10 G on intergalactic scales, we find that perturbations on galactic scales could have gone nonlinear at z ≃ 6. Finally, we discuss how primordial magnetic fields affect scenarios of structure formation with nonbaryonic dark matter.