Searching for Primordial Magnetic Fields with CMB B-modes
  Was the primordial universe magnetized? The answer to this question would
help explain the origin of micro-Gauss strength magnetic fields observed in
galaxies. It is also of fundamental importance in developing a complete theory
of the early universe. While there can be other signatures of cosmological
magnetic fields, a signature in the cosmic microwave background (CMB) would
prove their primordial origin. The B-mode polarization of CMB is particularly
promising in this regard because there are relatively few other sources of
B-modes, and because the vortical modes sourced by the primordial magnetic
field (PMF) survive diffusion damping up to a small fraction of the Silk
length. At present, the Planck temperature and polarization spectra combined
with the B-mode spectrum measured by the South Pole Telescope (SPT) constrain
the PMF strength to be no more than $\sim 1$ nano-Gauss (nG). Because of the
quartic scaling of the CMB anisotropy spectra with the PMF strength, this bound
will not change by much even with the significantly better measurements of the
B-mode spectrum by the Stage III and Stage IV CMB experiments. On the other
hand, tightening the bound well below the $1$ nG threshold would rule out the
purely primordial origin (requiring no dynamo action) of galactic fields.
Considering Faraday rotation, which converts some of the E-modes into B-modes
and scales linearly with the field strength, will help to achieve this goal. As
we demonstrate, the upcoming experiments, such as SPT-3G and the Simons
Observatory, will be sensitive to fields of $\sim 0.5$ nG strength thanks to
the mode-coupling signature induced by Faraday rotation. A future Stage IV
ground based experiment or a Space Probe will be capable of probing fields
below $0.1$ nG, and would detect a scale-invariant PMF of $0.2$ nG strength
without de-lensing or subtracting the galactic rotation measure.
