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Imprints of anisotropic inflation on the cosmic microwave background

We study the imprints of anisotropic inflation on the CMB temperature fluctuations and polarizations. The statistical anisotropy stems not only from the direction dependence of curvature and tensor perturbations, but also from the cross correlation between curvature and tensor perturbations, and the linear polarization of tensor perturbations. We show that off-diagonal $TB$ and $EB$ spectrum as well as on- and off-diagonal $TT, EE, BB, TE$ spectrum are induced from anisotropic inflation. We emphasize that the off-diagonal spectrum induced by the cross correlation could be a characteristic signature of anisotropic inflation.