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 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.
