  Gravitational waves from inflation induce polarization patterns in the cosmic
microwave background (CMB). It is known that there are only two types of
non-Gaussianities of the gravitaional waves in the most general scalar field
theories having second-order field equations. One originates from the inherent
non-Gaussianity in general relativity, and the other from a derivative coupling
between the Einstein tensor and a kinetic term of the scalar field. We
calculate polarization bispectra induced by these non-Gaussianities by
transforming them into separable forms by virtue of the Laplace transformation.
It is shown that future experiments can detect only the new one if the latter
coupling parameter takes an extremely large value, which, however, does not
cotradict the current observational data.
