Primordial magnetism in the CMB: Exact treatment of Faraday rotation and WMAP7 bounds

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 cosmic microwave background 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 bound for a range of parameters. Observations of the cosmic microwave background polarization at smaller angular scales are crucial to provide tighter constraints or a detection.