Primordial tensor non-Gaussianities from general single-field inflation with non-Bunch-Davies initial states

It has been found that the primordial non-Gaussianity of the curvature perturbation in the case of non-Bunch-Davies initial states can be enhanced compared with those in the case of the Bunch-Davies one due to the interactions among the perturbations on subhorizon scales. The purpose of the present paper is to investigate whether tensor non-Gaussianities can also be enhanced or not by the same mechanism. We consider general gravity theory in the presence of an inflaton, and evaluate the tensor auto-bispectrum and the cross-bispectrum involving one tensor and two scalar modes with the non-Bunch-Davies initial states for tensor modes. The crucial difference from the case of the scalar auto-bispectrum is that the tensor three-point function vanishes at the flattened momentum triangles. We point out that the cross-bispectrum can potentially be enhanced at non-trivial triangle shapes due to the non-Bunch-Davies initial states.