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

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 nonzero parity-odd (B-mode) polarization component. The Wilkinson Microwave Anisotropy Probe 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 6x10(-8) to 2x10(-6) G on a comoving length scale of 1 Mpc, depending on the power spectrum of the magnetic field.