Non-Gaussianity of a single scalar field in general covariant Hořava-Lifshitz gravity

Abstract

In this paper, we study non-Gaussianity generated by a single scalar field in slow-roll inflation in the framework of the non-relativistic general covariant Hořava-Lifshitz theory of gravity with the projectability condition and an arbitrary coupling constant $\lambda$, where $\lambda$ characterizes the deviation of the theory from general relativity (GR) in the infrared. We find that the leading effect of self-interaction, in contrary to the case of minimal scenario of GR, is in general of the order ${\hat{\alpha }}_n{\epsilon }^{3/2}$, where $\epsilon$ is a slow-roll parameter, and ${\hat{\alpha }}_n(n=3,5)$ are the dimensionless coupling coefficients of the six-order operators of the Lifshitz scalar, and have no contributions to power spectra and indices of both scalar and tensor. The bispectrum, comparing with the standard one given in GR, is enhanced, and gives rise to a large value of the nonlinearity parameter $f_{\text{NL}}$.We study how the modified dispersion relation with high order moment terms affects the evaluation of the mode function and in turn the bispectrum, and show explicitly that the mode function takes various asymptotic forms during different periods of its evolution. In particular, we find that it is in general of superpositions of oscillatory functions, instead of plane waves like in the minimal scenario of GR. This results in a large enhancement of the folded shape in the bispectrum.

Added new references and corrected some typos. 5 figures, revtex4. Phys. Rev. D86, 103523 (2012)

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• Post-Newtonian approximations in the Hořava-Lifshitz gravity with extra U(1) symmetry
• Inflationary cosmology with nonlinear dispersion relations
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• High-order Primordial Perturbations with Quantum Gravitational Effects
• Constructing analytical solutions of linear perturbations of inflation with modified dispersion relations
• Primordial Non-Gaussianity of Gravitational Waves in Hořava-Lifshitz Gravity
• Static post-Newtonian limits in non-projectable Hořava-Lifshitz gravity with an extra U(1) symmetry
• Gravitational collapse in Hořava-Lifshitz theory
• Effective matter dispersion relation in quantum covariant Horava-Lifshitz gravity