Effects of non-linearities on magnetic field generation

Abstract

Magnetic fields are present on all scales in the Universe. While we understand the processes which amplify the fields fairly well, we do not have a "natural" mechanism to generate the small initial seed fields. By using fully relativistic cosmological perturbation theory and going beyond the usual confines of linear theory we show analytically how magnetic fields are generated. This is the first analytical calculation of the magnetic field at second order, using gauge-invariant cosmological perturbation theory, and including all the source terms. To this end, we have rederived the full set of governing equations independently. Our results suggest that magnetic fields of the order of $10^{-30}$ G can be generated (although this depends on the small scale cut-off of the integral), which is largely in agreement with previous results that relied upon numerical calculations. These fields are likely too small to act as the primordial seed fields for dynamo mechanisms.

21 pages; v2: minor changes, added references; v3: version accepted for publication in JCAP

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Cited by in corpus (11)

• Magnetic field spectrum at cosmological recombination revisited
• Induced superhorizon tensor perturbations from anisotropic non-Gaussianity
• The primordial magnetic field in our cosmic backyard
• Generation of large-scale magnetic fields, non-Gaussianity, and primordial gravitational waves in inflationary cosmology
• A precise numerical estimation of the magnetic field generated around recombination
• Isocurvature initial conditions for second order Boltzmann solvers
• Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
• Magnetogenesis from isocurvature initial conditions
• Recombination era magnetic fields from axion dark matter
• Double power series method for approximating cosmological perturbations
• Contrasting formulations of cosmological perturbations in a magnetic FLRW cosmology