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

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.

13 pages. Accepted for publication in PRD

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• Tensor Non-Gaussianity Search: Current Status and Future Prospects
• Cosmic microwave background bispectrum of tensor passive modes induced from primordial magnetic fields
• Cosmic microwave background bispectrum of vector modes induced from primordial magnetic fields
• Probing correlations of early magnetic fields using mu-distortion
• CMB power spectra induced by primordial cross-bispectra between metric perturbations and vector fields
• Angular dependence of primordial trispectra and CMB spectral distortions
• Probing parity-odd bispectra with anisotropies of GW $V$ modes
• Wigner-Eckart theorem in cosmology: Bispectra for total-angular-momentum waves
• Primordial tensor bispectra in $\mu$-CMB cross-correlations
• Constraining graviton non-Gaussianity through the CMB bispectra