Footprint of two-form field: Statistical anisotropy in primordial gravitational waves

We study the observational signatures of a two-form field in 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 nonzero for hexadecapole and tetrahexacontapole, while the quadrupole moment vanishes. Since their amplitude can reach O(10-3) in the tensor-to-scalar ratio, we expect this novel prediction will be tested in the next generation of cosmic microwave background experiments.