Violation of the Rotational Invariance in the CMB Bispectrum

Abstract

There have been many works that verify the possibility of the small deviation of the statistical isotropy, e.g., the so-called “Axis of Evil”. The analyses of the power spectrum by employing the current CMB data suggest that the deviation of the statistical isotropy is about 10 % at most. As is well known, it might be difficult to explain such statistical anisotropy in the standard inflationary scenario. However, recently, there have been several works about the possibility of generating the statistically anisotropic primordial density fluctuations in order to introduce nontrivial dynamics of the vector field. Owing to the effect of fluctuations of the vector field, the primordial density fluctuations may have a small deviation from the statistical isotropy and also the deviation from the Gaussian statistics. Hence, we can expect that there are characteristic signals not only in the CMB power spectrum but also in the CMB bispectrum. With these motivations, we calculate the CMB statistically anisotropic bispectrum sourced from the curvature perturbations generated in the modified hybrid inflation scenario. Then, we find the peculiar configurations of the multipoles which never appear in the isotropic bispectrum, like off-diagonal components in the CMB power spectrum.