Compressible hydromagnetic nonlinearities in the predecoupling plasma

TL;DR

This paper investigates how large-scale curvature inhomogeneities influence the evolution of magnetic fields in the predecoupling plasma, deriving equations that describe their behavior and solutions in both physical and Fourier space.

Contribution

It introduces a novel effective description of magnetic field evolution considering compressible hydromagnetic nonlinearities influenced by curvature inhomogeneities.

Findings

Curvature inhomogeneities shift the magnetic diffusivity scale to lower wavenumbers.

Derived a nonlocal master equation for magnetic spectra in Fourier space.

Presented explicit solutions in physical and Fourier space.

Abstract

The adiabatic inhomogeneities of the scalar curvature lead to a compressible flow affecting the dynamics of the hydromagnetic nonlinearities. The influence of the plasma on the evolution of a putative magnetic field is explored with the aim of obtaining an effective description valid for sufficiently large scales. The bulk velocity of the plasma, computed in the framework of the LambdaCDM scenario, feeds back into the evolution of the magnetic power spectra leading to a (nonlocal) master equation valid in Fourier space and similar to the ones discussed in the context of wave turbulence. Conversely, in physical space, the magnetic power spectra obey a Schroedinger-like equation whose effective potential depends on the large-scale curvature perturbations. Explicit solutions are presented both in physical space and in Fourier space. It is argued that curvature inhomogeneities, compatible with the WMAP 7yr data, shift to lower wavenumbers the magnetic diffusivity scale.