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

TL;DR

This paper derives comprehensive formulas for calculating the CMB bispectra resulting from non-Gaussian tensor and vector perturbations, highlighting differences from scalar modes and the impact of flat-sky approximations.

Contribution

It provides the first complete set of analytic formulae for tensor and vector mode bispectra in the CMB, including all-sky and flat-sky analyses.

Findings

All-sky tensor and vector bispectra formulas are complex due to azimuthal angle dependence.

Flat-sky approximation simplifies the bispectrum calculations by removing azimuthal dependence.

Vector or tensor bispectrum of B-mode polarization vanishes in the squeezed limit unless parity is violated.

Abstract

We present a complete set of formulae for calculating the bispectra of CMB temperature and polarization anisotropies generated from non-Gaussianity in the vector and tensor mode perturbations. In the all-sky analysis it is found that the bispectrum formulae for the tensor and vector-mode non-Gaussianity formally take complicated forms compared to the scalar mode one because the photon transfer functions in the tensor and vector modes depend on the azimuthal angle between the direction of the wave number vector of the photon's perturbation and that of the line of sight. We demonstrate that flat-sky approximations remove this difficulty because this kind of azimuthal angle dependence apparently vanishes in the flat-sky limit. Through the flat-sky analysis, we also find that the vector or tensor bispectrum of $B$-mode polarization vanishes in the squeezed limit, unless the cosmological parity is violated at the nonlinear level.