Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-10-11
JHEP 1003:061,2010
Physics
High Energy Physics
High Energy Physics - Theory
7 pages, references added; v3: Typos corrected, minor changes to text and precise determination of the strong coupling scale.
Scientific paper
10.1007/JHEP03(2010)061
We confirm the recent claims that, in the infrared limit of Ho\v{r}ava-Lifshitz gravity, the scalar graviton becomes a ghost if the sound speed squared is positive on the flat de Sitter and Minkowski background. In order to avoid the ghost and tame the instability, the sound speed squared should be negative and very small, which means that the flow parameter $\lambda$ should be very close to its General Relativity (GR) value. We calculate the cubic interactions for the scalar graviton which are shown to have a similar structure with those of the curvature perturbation in k-inflation models. The higher order interactions become increasing important for a smaller sound speed squared, that is, when the theory approaches GR. This invalidates any linearized analysis and any predictability is lost in this limit as quantum corrections are not controllable. This pathological behaviour of the scalar graviton casts doubt on the validity of the projectable version of the theory.
Arroja Frederico
Koyama Kazuya
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