Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background

TL;DR

This paper investigates how primordial magnetic fields with a log-normal distribution influence cosmic microwave background anisotropies, providing new constraints on their strength and scale based on observational data.

Contribution

It introduces a model of primordial magnetic fields with a log-normal spectrum and analyzes their effects on CMB anisotropies, offering constraints different from previous power-law models.

Findings

Upper limit on magnetic field strength: B ≲ 3 nG.

Strongest constraints at scale k ≈ 10^{-2.5} Mpc^{-1}.

CMB data constrains primordial magnetic fields with a characteristic scale.

Abstract

We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of perturbations generated from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang, and ACBAR data sets, we find that the current CMB data set places the strongest constraint at $k\simeq 10^{-2.5}$ Mpc$^{-1}$ with the upper limit $B\lesssim 3$ nG.