Primordial Non-Gaussianity of Gravitational Waves in Ho\v{r}ava-Lifshitz Gravity

Understand

In this paper, we study 3-point correlation function of primordial gravitational waves generated in the de Sitter background in the framework of the general covariant Ho\v{r}ava-Lifshitz gravity with an arbitrary coupling constant $\lambda$.

• We find that, at cubic order, the interaction Hamiltonian receives contributions from four terms built of the 3-dimensional Ricci tensor $R_{ij}$ of the leaves $t = $ constant.
• In particular, the 3D Ricci scalar $R$ yields the same $k$-dependence as that in general relativity, but with different magnitude due to coupling with the $U(1)$ field $A$ and a UV history.
• Interestingly, the two terms $R_{ij}R^{ij}$ and $\left(\nabla^{i}R^{jk}\right)\left(\nabla_{i}R_{jk}\right)$ exhibit peaks at the squeezed limit.