Oscillating universe in Hořava-Lifshitz gravity

We study the dynamics of isotropic and homogeneous universes in the generalized Hořava-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 Λ. A bounce universe solution is obtained for Λ>0, K=±1 or Λ=0, K=-1, while an oscillation spacetime is found for Λ≥0, K=1, or Λ<0, K=±1. We also propose a quantum tunneling scenario from an oscillating spacetime to an inflationary universe, resulting in a macroscopic cyclic universe.