Yongqing Huang, Anzhong Wang, Razieh Yousefi, Tao Zhu
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, to the leading 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. The two terms $R_{ij} R^{ij}$ and $(\nabla^i R^{jk}) (\nabla_i R_{jk})$ exhibit a peak at the squeezed limit. The term $R^i_j R^j_k R^k_i$ favors the equilateral shape when spins of the three tensor fields are the same but peaks in between the equilateral and squeezed limits when spins are mixed. This is due to the effects of the polarization tensors. Hence, a detection of the squeezed shape or absence of in the bispectrum cannot rule out completely higher derivative gravity theories, at least for $R^2$ theories. The consistency with the recently-released Planck observations on non-Gaussianity is also discussed.
View original:
http://arxiv.org/abs/1304.1556
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