Abstract
Gravitational waves from inflation induce polarization patterns in the cosmic microwave background (CMB). It is known that there are only two types of non-Gaussianities of the gravitaional waves in the most general scalar field theories having second-order field equations. One originates from the inherent non-Gaussianity in general relativity, and the other from a derivative coupling between the Einstein tensor and a kinetic term of the scalar field. We calculate polarization bispectra induced by these non-Gaussianities by transforming them into separable forms by virtue of the Laplace transformation. It is shown that future experiments can detect only the new one if the latter coupling parameter takes an extremely large value, which, however, does not cotradict the current observational data.
Highlights
We calculated cosmic microwave background (CMB) temperature bispectrum induced by this mode and found that even if f5X takes such a large value, the signal-to-noise ratio of the resultant temperature bispectrum is too small to be detected, so that it would not contradict any current observational data
We show the shapes of the primordial non-Gaussianities and the B-mode reduced bispectrum Their shapes are similar in both general relativity and the new class of gravity in which G5X does not vanish
We calculated the B-mode auto-bispectrum induced by tensor perturbations produced during inflation in the early Universe based on the most general single field inflation model [24]
Summary
Inflation in the early Universe [1,2,3,4,5] produces both primordial density perturbations [6,7,8,9] and gravitational waves [10, 11] out of quantum fluctuations. (For a review of inflation, see e.g. [12].) The simplest model of slow-roll inflation predicts that they are almost Gaussian and that the primordial density perturbations have only small non-Gaussianities of the order of the slow-roll parameters [13, 14]. Primordial non-Gaussianities of the gravitational waves differ from those of the curvature perturbations They are known to be classified to only two types [24] in the framework of the generalized G-inflation [25] which is originally the most general single-field inflation model based on the Horndeski theory [26, 27] with second-order field equations. The other is originated from a certain kind of a non-minimal derivative coupling of the scalar field with the Einstein tensor Detection of the former would provide an evidence that the standard quantum field theory calculation in curved spacetime works well, whereas that of the latter would be a smoking gun of modification of gravity. Since primordial density perturbations cannot give rise to B-mode polarization [28,29,30,31], its primary auto-bispectrum just reflects the non-Gaussianities of gravitational waves.
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