Primordial magnetic fields from second-order cosmological perturbations: Tight coupling approximation

TL;DR

This paper investigates the generation of large-scale magnetic fields during the pre-recombination era through second-order cosmological perturbations, employing the tight coupling approximation to analyze the process.

Contribution

It introduces a detailed analysis of magnetic field generation from second-order perturbations using the tight coupling approximation, highlighting the role of vorticity and first-order perturbation products.

Findings

Magnetic fields of ~10^{-29} Gauss are generated on the horizon scale at recombination.

The process is driven by vorticity sourced by first-order perturbation products.

Further investigation is needed to confirm effectiveness on smaller scales.

Abstract

We explore the possibility of generating large-scale magnetic fields from second-order cosmological perturbations during the pre-recombination era. The key process for this is Thomson scattering between the photons and the charged particles within the cosmic plasma. To tame the multi-component interacting fluid system, we employ the tight coupling approximation. It is shown that the source term for the magnetic field is given by the vorticity, which signals the intrinsically second-order quantities, and the product of the first order perturbations. The vorticity itself is sourced by the product of the first-order quantities in the vorticity evolution equation. The magnetic fields generated by this process are estimated to be $\sim 10^{-29} $Gauss on the horizon scale at the recombination epoch. Although our rough estimate suggests that the current generation mechanism can work even on smaller scales, more careful investigation is needed to make clear whether it indeed works in a wide range of spatial scales.