Faraday Rotation Limits on a Primordial Magnetic Field from WMAP Five-Year Data

TL;DR

This paper uses WMAP 5-year data to set upper limits on the strength of a primordial magnetic field by analyzing its Faraday rotation effect on the cosmic microwave background's polarization.

Contribution

It provides new constraints on primordial magnetic fields by linking Faraday rotation-induced B-mode polarization to magnetic field strength limits.

Findings

Upper limits on magnetic field strength range from 6×10⁻⁸ to 2×10⁻⁶ G

Constraints depend on the magnetic field's power spectrum

Analysis assumes B-mode polarization is solely due to Faraday rotation

Abstract

A primordial magnetic field in the early universe will cause Faraday rotation of the linear polarization of the cosmic microwave background generated via Compton scattering at the surface of last scattering. This rotation induces a non-zero parity-odd (B-mode) polarization component. The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data puts an upper limit on the magnitude of the B-polarization power spectrum; assuming that the B-polarization signal is totally due to the Faraday rotation effect, the upper limits on the comoving amplitude of a primordial stochastic magnetic field range from $6 \times 10^{-8}$ to $2 \times 10^{-6}$ G on a comoving length scale of 1 Mpc, depending on the power spectrum of the magnetic field.