Footprint of Two-Form Field: Statistical Anisotropy in Primordial Gravitational Waves

We study the observational signatures of two-form field in the inflationary cosmology. In our setup a two-form field is kinetically coupled to a spectator scalar field and generates sizable gravitational waves and smaller curvature perturbation. We find that the sourced gravitational waves have a distinct signature: they are always statistically anisotropic and their spherical moments are non-zero for hexadecapole and tetrahexacontapole, while the quadrupole moment vanishes. Since their amplitude can reach $\mathcal{O}({10}^{-3})$ in the tensor-to-scalar ratio, we expect this novel prediction will be tested in the next generation of the CMB experiments.