Oscillating Bianchi IX Universe in Horava-Lifshitz Gravity
  We study a vacuum Bianchi IX universe in the context of Ho\v{r}ava-Lifshitz
(HL) gravity. In particular, we focus on the classical dynamics of the universe
and analyze how anisotropy changes the history of the universe. For small
anisotropy, we find an oscillating universe as well as a bounce universe just
as the case of the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime.
However, if the initial anisotropy is large, we find the universe which ends up
with a big crunch after oscillations if a cosmological constant $\Lambda$ is
zero or negative. For $\Lambda>0$, we find a variety of histories of the
universe, that is de Sitter expanding universe after oscillations in addition
to the oscillating solution and the previous big crunch solution. This fate of
the universe shows sensitive dependence of initial conditions, which is one of
the typical properties of a chaotic system. If the initial anisotropy is near
the upper bound, we find the universe starting from a big bang and ending up
with a big crunch for $\Lambda\leq 0$, while de Sitter expanding universe
starting from a big bang for $\Lambda>0$.
