Violation of the Rotational Invariance in the CMB Bispectrum

We investigate a statistical anisotropy on the Cosmic Microwave Background (CMB) bispectrum, which can be generated from the primordial non-Gaussianity induced by quantum fluctuations of a vector field. We find new configurations in the multipole space of the CMB bispectrum given by l(1) = l(2) + l(3) + 2, vertical bar l(2) - l(3)vertical bar - 2 and their permutations, which violate the rotational invariance, such as an off-diagonal configuration in the CMB power spectrum. We also find that in a model presented by Yokoyama and Soda (2008), the amplitude of the statistically anisotropic bispectrum in the above configurations becomes as large as that in other configurations such l(1) = l(2) + l(3). As a result, it might be possible to detect these contributions in future experiments, which would give us novel information about the physics of the early Universe.