Primordial Non-Gaussianities of Gravitational Waves in the Most General Single-Field Inflation Model with Second-Order Field Equations

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in 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 $h_{ij}$ 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 detection experiments.

Figure 1

${\mathcal{A}}_{(\mathrm{new})}^{+++}(1,k_2/k_1,k_3/k_1)(k_2/k_1{)}^{-1}(k_3/k_1{)}^{-1}$ as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to unity for equilateral configurations $k_2/k_1=k_3/k_1=1$.

Figure 2

${\mathcal{A}}_{(\mathrm{GR})}^{+++}(1,k_2/k_1,k_3/k_1)(k_2/k_1{)}^{-1}(k_3/k_1{)}^{-1}$ as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to unity for equilateral configurations $k_2/k_1=k_3/k_1=1$.