A stable anisotropic inflationary solution exists in the Saez-Ballester theory, but it is equivalent to the known Kanno-Soda-Watanabe solution and has a too-large tensor-to-scalar ratio.
Imprints of anisotropic inflation on the cosmic microwave background
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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.
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Anisotropic power-law inflation for the S\'aez-Ballester theory non-minimally coupled to a vector field
A stable anisotropic inflationary solution exists in the Saez-Ballester theory, but it is equivalent to the known Kanno-Soda-Watanabe solution and has a too-large tensor-to-scalar ratio.