Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum

Although cosmological observations suggest that the fluctuations of seed fields are almost Gaussian, the possibility of a small deviation of their fields from Gaussianity is widely discussed. Theoretically, there exist numerous inflationary scenarios which predict large and characteristic non-Gaussianities in the primordial perturbations. These model-dependent non-Gaussianities act as sources of the Cosmic Microwave Background (CMB) bispectrum; therefore, the analysis of the CMB bispectrum is very important and attractive in order to clarify the nature of the early Universe. Currently, the impacts of the primordial non-Gaussianities in the scalar perturbations, where the rotational and parity invariances are kept, on the CMB bispectrum have been well-studied. However, for a complex treatment, the CMB bispectra generated from the non-Gaussianities, which originate from the vector- and tensor-mode perturbations and include the violation of the rotational or parity invariance, have never been considered in spite of the importance of this information. On the basis of our current studies, this thesis provides the general formalism for the CMB bispectrum sourced by the non-Gaussianities not only in the scalar-mode perturbations but also in the vector- and tensor-mode perturbations. Applying this formalism, we calculate the CMB bispectrum from two scalars and a graviton correlation and that from primordial magnetic fields, and we then outline new constraints on these amplitudes. Furthermore, this formalism can be easily extended to the cases where the rotational or parity invariance is broken. We also compute the CMB bispectra from the non-Gaussianities of the curvature perturbations with a preferred direction and the graviton non-Gaussianities induced by the parity-violating Weyl cubic terms. We also present some unique impacts to the violation of these invariances on the CMB bispectrum.