Magnetic field spectrum at cosmological recombination revisited

Abstract

If vector type perturbations are present in the primordial plasma before recombination, the generation of magnetic fields is known to be inevitable through the Harrison mechanism. In the context of the standard cosmological perturbation theory, non-linear couplings of first-order scalar perturbations create second-order vector perturbations, which generate magnetic fields. Here we reinvestigate the generation of magnetic fields at second-order in cosmological perturbations on the basis of our previous study, and extend it by newly taking into account the time evolution of purely second-order vector perturbations with a newly developed second-order Boltzmann code. We confirm that the amplitude of magnetic fields from the product-terms of the first-order scalar modes is consistent with the result in our previous study. However, we find, both numerically and analytically, that the magnetic fields from the purely second-order vector perturbations partially cancel out the magnetic fields from one of the product-terms of the first-order scalar modes, in the tight coupling regime in the radiation dominated era. Therefore, the amplitude of the magnetic fields on small scales, $k\gtrsim 10h{\mathrm{Mpc}}^{-1}$, is smaller than the previous estimates. The amplitude of the generated magnetic fields at cosmological recombination is about $B_{\mathrm{rec}}=5.0\times 10^{-24}\mathrm{Gauss}$ on $k=5.0\times 10^{-1}h{\mathrm{Mpc}}^{-1}$. Finally, we discuss the reason of the discrepancies that exist in estimates of the amplitude of magnetic fields among other authors.

22 pages, 4 figures, This article draws heavily from arXiv:astro-ph/0701329, and is essentially a revised version of that paper which has not been published in a journal, Accepted for publication in PRD

References in corpus (16)

• Generation of Large-Scale Magnetic Fields in Single-Field Inflation
• Magnetic fields from inflation?
• Cosmological Magnetic Field: a fossil of density perturbations in the early universe
• Adding helicity to inflationary magnetogenesis
• Universal upper limit on inflation energy scale from cosmic magnetic field
• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• Cosmological Perturbations at Second Order and Recombination Perturbed
• Observable primordial vector modes
• Cosmological magnetic fields from nonlinear effects
• Primordial magnetic fields from second-order cosmological perturbations: Tight coupling approximation
• Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations
• Cosmological Structure Formation Creates Large-Scale Magnetic Fields
• Geodesic "curve"-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing
• Electromagnetic Properties of the Early Universe
• Primordial magnetic fields from self-ordering scalar fields
• Constraining primordial vector mode from B-mode polarization

Cited by in corpus (4)

• Non-comoving Cosmology
• Mean Energy Density of Photogenerated Magnetic Fields Throughout the Epoch of Reionization
• Observable cosmological vector mode in the dark ages
• Magnetogenesis from isocurvature initial conditions