Hunting for Statistical Anisotropy in Tensor Modes with B-mode Observations

We investigate a possibility of constraining statistical anisotropies of the primordial tensor perturbations by using future observations for the Cosmic Microwave Background (CMB) B-mode polarization. By parameterizing a statistically-anisotropic tensor power spectrum as $P_h ({\boldsymbol{k}}) = P_h (k) \sum_n g_n \cos^n \theta_{\boldsymbol{k}}$, where $\theta_{\boldsymbol{k}}$ is an angle of the direction of $\hat{k}={\boldsymbol{k}}/k$ from a preferred direction, we find that it would be possible for future B-mode observations such as CMB-S4 to detect the tensor statistical anisotropy at the level of $g_n \sim {\mathcal O} (0.1)$.