Observational signatures of anisotropic inflationary models

We study observational signatures of two classes of anisotropic inflationary models in which an inflaton field couples to (i) a vector kinetic term F mu nu F mu nu and (ii) a two-form kinetic term H mu nu lambda H mu nu lambda. We compute the corrections from the anisotropic sources to the power spectrum of gravitational waves as well as the two-point cross correlation between scalar and tensor perturbations. The signs of the anisotropic parameter g(*) are different depending on the vector and the two-form models, but the statistical anisotropies generally lead to a suppressed tensor-to-scalar ratio r and a smaller scalar spectral index n(s) in both models. In the light of the recent Planck bounds of n(s) and r, we place observational constraints on several different inflaton potentials such as those in chaotic and natural inflation in the presence of anisotropic interactions. In the two-form model we also find that there is no cross correlation between scalar and tensor perturbations, while in the vector model the cross correlation does not vanish. The non-linear estimator f(NL) of scalar non-Gaussianities in the two-form model is generally smaller than that in the vector model for the same orders of vertical bar g(*)vertical bar, so that the former is easier to be compatible with observational bounds of non-Gaussianities than the latter.