Primordial Magnetism in the CMB: Exact Treatment of Faraday Rotation and WMAP7 Bounds

TL;DR

This paper provides an exact numerical analysis of how primordial magnetic fields induce B-mode polarization in the CMB via Faraday rotation, deriving constraints from WMAP7 data and emphasizing the importance of smaller-scale observations.

Contribution

It introduces a full numerical solution to the CMB radiative transport equations for magnetic field-induced B-modes, improving constraints beyond previous bounds.

Findings

WMAP7 data constrains primordial magnetic fields more tightly than BBN bounds.

Faraday rotation causes distinctive frequency-dependent B-modes.

Smaller angular scale CMB polarization observations are essential for tighter constraints.

Abstract

Faraday rotation induced B-modes can provide a distinctive signature of primordial magnetic fields because of their characteristic frequency dependence and because they are only weakly damped on small scales, allowing them to dominate B-modes from other sources. By numerically solving the full CMB radiative transport equations, we study the B-mode power spectrum induced by stochastic magnetic fields that have significant power on scales smaller than the thickness of the last scattering surface. Constraints on the magnetic field energy density and inertial scale are derived from WMAP 7-year data, and are stronger than the big bang nucleosynthesis (BBN) bound for a range of parameters. Observations of the CMB polarization at smaller angular scales are crucial to provide tighter constraints or a detection.