Joint constraint on primordial gravitational waves and polarization rotation angle with current CMB polarization data

Cosmological CPT violation will rotate the polarized direction of CMB photons, convert partial CMB E mode into B mode and vice versa. It will generate non-zero EB, TB spectra and change the EE, BB, TE spectra. This phenomenon gives us a way to detect the CPT-violation signature from CMB observations, and also provides a new mechanism to produce B mode polarization. In this paper, we perform a global analysis on tensor-to-scalar ratio $r$ and polarization rotation angles based on current CMB datasets with both low $\mathrm{\ell }$ (Planck, BICEP2/Keck Array) and high $\mathrm{\ell }$ (POLARBEAR, SPTpol, ACTPol). Benefited from the high precision of CMB data, we obtain the isotropic rotation angle $\bar{\alpha }=-{0.01}^{\circ }\pm {0.37}^{\circ }$ at 68% C.L., the variance of the anisotropic rotation angles $C^{\alpha }(0)<0.0032{\mathrm{r}\mathrm{a}\mathrm{d}}^2$, the scale invariant power spectrum $D^{\alpha\alpha}_{\ell \in [2, 350]}<4.71\times 10^{-5} ,$\mathrm{r}\mathrm{a}\mathrm{d}$^2$and$r<0.057$ at 95% C.L… Our result shows that with the polarization rotation effect, the 95% upper limit on $r$ gets tightened by 17%.