Large-scale magnetic fields from density perturbations

We derive the minimal seed magnetic field which unavoidably arises in the radiation and matter eras, prior to recombination, by the rotational velocity of ions and electrons, gravitationally induced by the nonlinear evolution of primordial density perturbations. The resulting magnetic field power spectrum is fully determined by the amplitude and spectral index of density perturbations. The rms amplitude of the seed field at recombination is $B\approx {10}^{-23}(\lambda /\mathrm{M}\mathrm{p}\mathrm{c}{)}^{-2}\mathrm{G}$, on comoving scales $\lambda \gtrsim 1\mathrm{M}\mathrm{p}\mathrm{c}$.

Figure 1

Power spectrum of the magnetic field at recombination as a function of the comoving wave number. The upper and lower curves refer to the case with or without Silk damping included, respectively.