Testing parity-violating mechanisms with cosmic microwave background experiments

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 nonzero $TB/EB$ correlations are found. To do so, we evaluate the correlation matrix, including new $TB\mathrm{\text{−}}EB$ covariances. We find that the effects of these two mechanisms on the CMB are highly orthogonal, and can thus be distinguished fairly well in the case of a high-signal-to-noise detection of $TB/EB$ correlations. Appendix B evaluates the relative sensitivities of the $BB$, $TB$, and $EB$ signals for detecting a chiral gravitational-wave background.

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 four 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 nondetectable. The WMAP-5 curve lies entirely above the nondetection line.

Figure 3

Diagonal ($TB$, $TB$ and $EB$, $EB$) summands of Eq. (6), 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. (9), 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 $\Delta \alpha =5^{\prime }$ (solid blue curves).

Figure 6

Constraints on the allowed $\Delta \alpha \mathrm{\text{−}}\Delta \chi$ parameter space are shown for the case of null detection with different instruments. The solid-line ellipses on each plot are for the fiducial value of zero for both parameters, and for the following values of tensor-to-scalar ratios (going from the narrowest to the widest ellipse in the $\Delta \chi$ direction): 0.22, 0.1, and 0.06. The dot-dashed ellipse in each plot is for $r=0.22$, for a model with $\Delta \chi =0.2$ and $\Delta \alpha =5^{\prime \prime }$. In both models, the tilt of the ellipses is almost negligible, which means that the two $P$-violating mechanisms are separable to high accuracy, provided there is detection with high statistical significance. Thus, the constraints on both parameters are almost the same as those calculated in the previous sections.

Figure 7

$BB$ power spectra from primordial GWs (dashed lines), and from WL of the primordial $E$ modes (solid lines), for $r=0.22$ (red, bottom solid and top dashed lines), $r=0.1$ (blue, middle lines), and $r=0.06$ (green, top solid and bottom dashed lines). The dotted black line is the appropriately normalized noise power spectrum for CMBPol. Note that the noise dominates above $l\sim 100$.