Testing Parity-Violating Mechanisms with Cosmic Microwave Background Experiments

TL;DR

The paper addresses how to distinguish parity-violating effects in the CMB arising from cosmological birefringence ($Δα$) and gravitational chirality ($Δχ$) by analyzing TB and EB correlations. It defines a chiral parameter $Δχ$ via differences in left/right tensor power and a rotation angle $Δα$ for CB, then forecasts constraints with a Fisher-matrix approach using TB/EB covariances for experiments from WMAP-5 to a cosmic-variance-limited case. The results show that the TB/EB signatures of chirality and CB are largely orthogonal, enabling separation with high significance when TB/EB is detected, and they quantify the expected sensitivities for each instrument. This work provides a practical framework for upcoming CMB polarization measurements to test fundamental parity-violating physics and to falsify or confirm proposed mechanisms. It also highlights that, while current data are insufficient to constrain $Δχ$, future missions could jointly bound or detect both $Δχ$ and $Δα$ with minimal degeneracy.

Abstract

Chiral gravity and cosmological birefringence both provide physical mechanisms to produce parity-violating TB and EB correlations in the cosmic microwave background (CMB) temperature/polarization. Here, we study how well these two mechanisms can be distinguished if non-zero TB/EB correlations are found. To do so, we evaluate the correlation matrix, including new TB-EB covariances. We find that the effects of these two mechanisms on the CMB are highly orthogonal, and can thus be distinguished fairly well in case of a high--signal-to-noise detection of TB/EB correlations. An Appendix evaluates the relative sensitivities of the BB, TB, and EB signals for detecting a chiral gravitational-wave background.

Figures (6)

• Figure 1: B-mode power spectra for $r=0.22$ and $\Delta \chi =0.2$.
• Figure 2: 1$\sigma$ error on the gravitational chirality parameter $\Delta \chi$, for five different CMB experiments, for the fiducial value of $\Delta \chi=0$. The horizontal dotted line is at $\sigma _{\Delta \chi}=1$ and represents maximal P violation. In the region above this line, the chirality is non-detectable. The WMAP-5 curve lies entirely above the non-detection line.
• Figure 3: Diagonal (TB,TB and EB,EB) summands of Eq. (\ref{['sigma_matrix_chi']}), for $r=0.22$, are plotted against the multipole $l$ to show that the constraint to $\Delta \chi$ comes primarily from the TB power spectrum at $l\sim 7$.
• Figure 4: Diagonal (TB,TB and EB,EB) summands of Eq. (\ref{['sigma_matrix_alpha']}), for $r=0.22$, are plotted against the multipole $l$ to show that the constraints to $\Delta \alpha$ from future CMB experiments will come primarily from $l$'s of $\sim$100, 500, or 700 (depending on the instrument).
• Figure 5: We show TB and EB power spectra from chiral GWs for $\Delta \chi = 0.2$ and $r=0.22$ (dashed red curves) and from cosmological birefringence for $\Delta \alpha=5'$ (solid blue curves).