POLARBEAR Constraints on Cosmic Birefringence and Primordial Magnetic
  Fields
  We constrain anisotropic cosmic birefringence using four-point correlations
of even-parity $E$-mode and odd-parity $B$-mode polarization in the cosmic
microwave background measurements made by the POLARization of the Background
Radiation (POLARBEAR) experiment in its first season of observations. We find
that the anisotropic cosmic birefringence signal from any parity-violating
processes is consistent with zero. The Faraday rotation from anisotropic cosmic
birefringence can be compared with the equivalent quantity generated by
primordial magnetic fields if they existed. The POLARBEAR nondetection
translates into a 95% confidence level (C.L.) upper limit of 93 nanogauss (nG)
on the amplitude of an equivalent primordial magnetic field inclusive of
systematic uncertainties. This four-point correlation constraint on Faraday
rotation is about 15 times tighter than the upper limit of 1380 nG inferred
from constraining the contribution of Faraday rotation to two-point
correlations of $B$-modes measured by Planck in 2015. Metric perturbations
sourced by primordial magnetic fields would also contribute to the $B$-mode
power spectrum. Using the POLARBEAR measurements of the $B$-mode power spectrum
(two-point correlation), we set a 95% C.L. upper limit of 3.9 nG on primordial
magnetic fields assuming a flat prior on the field amplitude. This limit is
comparable to what was found in the Planck 2015 two-point correlation analysis
with both temperature and polarization. We perform a set of systematic error
tests and find no evidence for contamination. This work marks the first time
that anisotropic cosmic birefringence or primordial magnetic fields have been
constrained from the ground at subdegree scales.
