Can primordial parity violation explain the observed cosmic birefringence?

Recently, the cross-correlation between $E$- and $B$-mode polarization of the cosmic microwave background, which is well explained by cosmic birefringence with rotation angle $\beta \approx 0.3\mathrm{deg}$, has been found in cosmic microwave background polarization data. We carefully investigate the possibility of explaining the observed $EB$ correlation by the primordial chiral gravitational waves, which can be generated in the parity-violating theories in the primordial Universe. We found that the chiral gravitational wave scenario does not work due to the overproduction of the $BB$ autocorrelation, which far exceeds the observed one by SPTPol and POLARBEAR.

Figure 1

Left panel: $EB$ angular power spectra $D_{\ell }^{EB}\equiv \ell (\ell +1)C_{\ell }^{EB}/(2\pi )$ against multipole $\ell$. The black line denotes $D_{\ell }^{EB}$ induced by cosmic birefringence with rotation angle of $\beta =0.3\mathrm{deg}$ and we try reproducing it. The other colored lines represent individual $D_{\ell }^{EB}$ contributions produced by each term in the CGW spectrum (1) with the parameters tuned to match the peaks of the black line. Right panel: $BB$ angular power spectra $D_{\ell }^{BB}$ produced by the same CGWs as the left panel in the same color. Blue and red plots represent the actual $BB$ power spectra observed by SPTPol and POLARBEAR, which include foreground emissions, and any $D_{\ell }^{BB}$ prediction above them should be excluded. Circle dots and vertical bars show central values and $1\sigma (68\%)$ uncertainties, respectively. For the plots with negative center values, we show 95% confidence level upper bound with inverted triangles.

Figure 2

Ratios of maximum $D_{\ell }^{BB}$ to maximum $D_{\ell }^{EB}$ against varied width parameter $\sigma$ of ${\mathcal{P}}_h^R(k)$. The color scheme is the same as Fig. 1. The ratio is always larger than 21.5, while it should be at least smaller than 2.4 to explain the observed $EB$ without overproducing the $BB$ spectrum.