Anisotropic non-Gaussianity from a two-form field

We study an inflationary scenario with a two-form field to which an inflaton couples nontrivially. First, we show that anisotropic inflation can be realized as an attractor solution and that the two-form hair remains during inflation. A statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing the in-in formalism based on the interacting Hamiltonians. We find that the nonlinear estimators f_NL and τ_NL are correlated with the amplitude g_* of the statistical anisotropy in the power spectrum. Unlike the vector models, both f_NL and τ_NL vanish in the squeezed limit. However, the estimator f_NL can reach the order of 10 in the equilateral and enfolded limits. These results are consistent with the latest bounds on f_NL constrained by Planck.