Tensor Non-Gaussianity Search: Current Status and Future Prospects
  Primordial gravitational waves (GWs) are said to be a smoking gun in cosmic
inflation, while, even if they are detected, the specification of their origins
are still required for establishing a true inflationary model. Testing
non-Gaussianity in the tensor-mode anisotropies of the cosmic microwave
background (CMB) is one of the most powerful ways to identify sources of GW
signals. In this paper, we review studies searching for tensor
non-Gaussianities employing the CMB bispectrum and forecast future
developments. No significant signal has so far been found from temperature and
E-mode polarization data, while orders-of-magnitude improvements in detection
limits can be achieved by adding the information of B-mode polarization. There
is already an established methodology for bispectrum estimation, which
encourages a follow-up investigation with next-decadal CMB B-mode surveys.
