Testing parity-violating physics from cosmic rotation power
  reconstruction
  We study the reconstruction of the cosmic rotation power spectrum produced by
parity-violating physics, with an eye to ongoing and near future cosmic
microwave background (CMB) experiments such as BICEP Array, CMBS4, LiteBIRD and
Simons Observatory. In addition to the inflationary gravitational waves and
gravitational lensing, measurements of other various effects on CMB
polarization open new window into the early Universe. One of these is
anisotropies of the cosmic polarization rotation which probes the Chern-Simons
term generally predicted by string theory. The anisotropies of the cosmic
rotation are also generated by the primordial magnetism and in the Standard
Model extention framework. The cosmic rotation anisotropies can be
reconstructed as quadratic in CMB anisotropies. However, the power of the
reconstructed cosmic rotation is a CMB four-point correlation and is not
directly related to the cosmic-rotation power spectrum. Understanding all
contributions in the four-point correlation is required to extract the cosmic
rotation signal. Assuming a scale-invariant rotation spectrum motivated by the
inflationary cosmic-rotation models, we employ simulation to quantify each
contribution to the four-point correlation and find that (1) a secondary
contraction of the trispectrum increases the total signal-to-noise, (2) a bias
from the lensing-induced trispectrum is significant compared to the statistical
errors in, e.g., LiteBIRD and CMBS4-like experiments, (3) the use of a
realization-dependent estimator decreases the statistical errors by 10%-20%,
depending on experimental specifications, and (4) other higher-order
contributions are negligible at least for near future experiments.
