Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model

TL;DR

This paper analyzes the primordial non-Gaussianities of gravitational waves in the most general single-field inflation model, revealing only two shapes in the graviton bispectrum, which aids in observational identification.

Contribution

It provides a complete characterization of the cubic action for tensor perturbations in generalized G-inflation, identifying the specific shapes of non-Gaussianities.

Findings

Only two shapes (squeezed and equilateral) appear in the graviton bispectrum.

The cubic action simplifies to two main contributions, one identical to Einstein gravity.

These results can help distinguish inflationary models through CMB and gravitational wave observations.

Abstract

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in generalized G-inflation, i.e., the most general single-field inflation model with second order field equations. It is shown that the most general cubic action for the tensor perturbation (gravitational wave) $h_{ij}$ is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each $h_{ij}$. The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct gravitational wave detection experiments.