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.