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

Author:Maresuke Shiraishi
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo

(7.1)

and a normalization as .

7.1 Statistically-Anisotropic Non-Gaussianity in Curvature Perturbations

In this section, we briefly review the mechanism of generating the statistically anisotropic bispectrum induced by primordial curvature perturbations proposed in Ref. [14], where the authors set the system like the hybrid inflation wherein there are two scalar fields: inflaton and waterfall field , and a vector field coupled with a waterfall field. The action is given by

(7.2)

Here, is the field strength of the vector field , is the potential of fields and denotes a gauge coupling. To guarantee the isotropy of the background Universe, we need the condition that the energy density of the vector field is negligible in the total energy of the Universe and we assume a small expectation value of the vector field. Therefore, we neglect the effect of the vector field on the background dynamics and also the evolution of the fluctuations of the inflaton. In the standard hybrid inflation (only with the inflaton and the waterfall field), the inflation suddenly ends owing to the tachyonic instability of the waterfall field, which is triggered when the inflaton reaches a critical value . In the system described using Eq. (7.2), however, may fluctuate owing to the fluctuation of the vector field and it generates additional curvature perturbations.

Using the formalism [27–32], the total curvature perturbation on the uniform-energy-density hypersurface at the end of inflation can be estimated in terms of the perturbation of the -folding number as

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.