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 inflationary motivated 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.

Figure 1

Cross power spectrum between the input and reconstructed cosmic-rotation fluctuations, divided by the input cosmic-rotation spectrum with the Monte Carlo errors (the standard deviation of 100 realizations divided by $\sqrt{100}$). The rotated CMB map is created according to Eq. (10) (linear) or Eq. (1) (full). The “lensed weight” and “rotated-lensed weight” denote the cases with the lensed and rotated-lensed CMB spectra in the weight function of Eq. (12), respectively.

Figure 2

Angular power spectrum of the reconstructed cosmic rotation with subtraction of the disconnected bias, N1 term and lensing bias (black points) with the $1\sigma$ full-sky measured error in the reconstruction for one realization (Left: BK/LiteBIRD–like noise, Right: CMBS4-like noise). We use 100 realizations of the simulated maps and the Monte Carlo error is 10% of the error bars. We also show the disconnected bias (blue), N1 term (red), lensing bias (green), and the input rotation power spectrum (magenta). The dashed line shows the negative value.

Figure 3

Angular power spectrum of the reconstructed cosmic rotation after the subtraction of the disconnected bias, N1 term, lensing bias and input cosmic-rotation power spectrum (black) with the $1\sigma$ full-sky measured error for one realization (Left: BK/LiteBIRD–like noise, Right: CMBS4-like noise). We use 100 realizations of the simulated maps and the Monte Carlo error is 10% of the error bars. We also show the case with the lensed CMB power spectrum in the weight function of Eq. (12) (lensed weight).

Figure 4

The variance of the reconstructed rotation spectrum with the realization-dependent disconnected bias (RDN0) divided by that with the analytic disconnected bias (N0). We show the cases with the BK/LiteBIRD–like and CMBS4-like noise.

Figure 5

Test of the Gaussian variance. We show the variances of the reconstructed rotation spectrum with the realization-dependent disconnected bias (RDN0) and with the analytic disconnected bias (N0). They are divided by $2({\widehat{C}}_L^{\alpha \alpha }{)}^2$. The black lines show the case when the reconstructed power spectrum is described as a Gaussian statistics. Both the BK/LiteBIRD–like (solid) and CMBS4-like noise cases (dashed) are plotted.

Figure 6

Cumulative signal-to-noise ratio of the cosmic-rotation power spectrum amplitude with and without the N1 term (Left: BK/LiteBIRD–like noise, Right: CMBS4-like noise). We show the cases with different minimum multipole of the rotation spectrum.