The full contribution of a stochastic background of magnetic fields to CMB anisotropies

TL;DR

This paper investigates how a stochastic background of primordial magnetic fields influences CMB anisotropies, providing exact spectral expressions and analyzing scalar, vector, and tensor contributions across different spectral indices.

Contribution

It offers exact Fourier spectra for the energy-momentum of primordial magnetic fields and analyzes their impact on CMB anisotropies, including scalar, vector, and tensor perturbations.

Findings

Scalar contribution dominates CMB temperature anisotropies.

Vector contribution becomes significant at higher multipoles.

Analytic estimates for scalar contributions are provided.

Abstract

We study the contribution of a stochastic background (SB) of primordial magnetic fields (PMF) on the anisotropies in temperature and polarization of the cosmic microwave background radiation (CMB). A SB of PMF modelled as a fully inhomogeneous component induces non-gaussian scalar, vector and tensor metric linear perturbations. We give the exact expressions for the Fourier spectra of the relevant energy-momentum components of such SB, given a power-law dependence parametrized by a spectral index $n_B$ for the magnetic field power spectrum cut at a damping scale $k_D$. For all the values of $n_B$ considered here, the contribution to the CMB temperature pattern by such a SB is dominated by the scalar contribution and then by the vector one at higher multipoles. We also give an analytic estimate of the scalar contribution to the CMB temperature pattern.