  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 |g_*|, so that the
former is easier to be compatible with observational bounds of
non-Gaussianities than the latter.
