Oscillating Universe in Horava-Lifshitz Gravity

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We study the dynamics of isotropic and homogeneous universes in the generalized Ho\v{r}ava-Lifshitz gravity, and classify all possible evolutions of vacuum spacetime.

• In the case without the detailed balance condition, we find a variety of phase structures of vacuum spacetimes depending on the coupling constants as well as the spatial curvature $K$ and a cosmological constant $\Lambda$.
• A bounce universe solution is obtained for $\Lambda> 0, K=\pm 1$ or $\Lambda= 0, K=- 1$, while an oscillation spacetime is found for $\Lambda\geq 0, K=1$, or $\Lambda< 0, K=\pm 1$.
• We also propose a quantum tunneling scenario from an oscillating spacetime to an inflationary universe, resulting in a macroscopic cyclic universe.