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 tau(NL) are correlated with the amplitude g(*) of the statistical anisotropy in the power spectrum. Unlike the vector models, both f(NL) and tau(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. DOI: 10.1103/PhysRevD.87.083520