Primordial Non-Gaussianity of Gravitational Waves in Hořava-Lifshitz Gravity

Abstract

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 Hořava-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. We show that this is due to the effects of the polarization tensors. The signal generated by the fourth term, $R_j^i{R}_k^j{R}_i^k$, 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. The consistency with the recently-released Planck observations on non-Gaussianity is also discussed and is found that ${\left(H/M_{\ast }\right)}^2\left(H/M_{pl}\right)\le 10^{-8}$, where $M_{\ast }$ denotes the suppression energy of high-order operators, $M_{pl}$ the Planck mass, and $H$ the energy of inflation.

revtex4, 16 figures. Version to appear in Phys. Rev. D

References in corpus (12)

• Quantum Gravity at a Lifshitz Point
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Horava-Lifshitz Cosmology: A Review
• General Covariance in Gravity at a Lifshitz Point
• An Alternative Approach for General Covariant Horava-Lifshitz Gravity and Matter Coupling
• Polarizing primordial gravitational waves by parity violation
• Cosmology in nonrelativistic general covariant theory of gravity
• Stability, ghost, and strong coupling in nonrelativistic general covariant theory of gravity with $\lambda \ne 1$
• Inflation in general covariant Hořava-Lifshitz gravity without projectability
• Solar system tests and interpretation of gauge field and Newtonian prepotential in general covariant Hořava-Lifshitz gravity
• Static post-Newtonian limits in non-projectable Hořava-Lifshitz gravity with an extra U(1) symmetry
• Non-Gaussianity of a single scalar field in general covariant Hořava-Lifshitz gravity

Cited by in corpus (15)

• Hořava Gravity at a Lifshitz Point: A Progress Report
• An inflationary model with small scalar and large tensor nongaussianities
• Effects of parity violation on non-gaussianity of primordial gravitational waves in Hořava-Lifshitz gravity
• Probing non-Gaussian Stochastic Gravitational Wave Backgrounds with LISA
• Tensor non-Gaussianity in chiral scalar-tensor theories of gravity
• Probing the inflationary particle content: extra spin-2 field
• Squeezed tensor non-Gaussianity in non-attractor inflation
• Non-adiabatic Evolution of Primordial Perturbations and non-Gaussinity in Hybrid Approach of Loop Quantum Cosmology
• Primordial non-Gaussianities of gravitational waves beyond Horndeski
• Inflationary perturbation spectrum in extended effective field theory of inflation
• Primordial Tensor Non-Gaussianity from Massive Gravity
• Inflationary perturbation spectra at next-to-leading slow-roll order in effective field theory of inflation
• Breaking parity: the case of the trispectrum from chiral scalar-tensor theories of gravity
• Effective matter dispersion relation in quantum covariant Horava-Lifshitz gravity
• Tensor bispectrum mediated by an excited scalar field during inflation