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We present a complete set of formulae for calculating the bispectra of CMBtemperature and polarization anisotropies generated from non-Gaussianity in thevector and tensor mode perturbations. In the all-sky analysis it is found thatthe bispectrum formulae for the tensor and vector-mode non-Gaussianity formallytake complicated forms compared to the scalar mode one because the photontransfer functions in the tensor and vector modes depend on the azimuthal anglebetween the direction of the wave number vector of the photon's perturbationand that of the line of sight. We demonstrate that flat-sky approximationsremove this difficulty because this kind of azimuthal angle dependenceapparently vanishes in the flat-sky limit. Through the flat-sky analysis, wealso find that the vector or tensor bispectrum of $B$-mode polarizationvanishes in the squeezed limit, unless the cosmological parity is violated atthe nonlinear level.

Analytic formulae of the CMB bispectra generated from non-Gaussianity in the tensor and vector perturbations