$f(R)$ theory and geometric origin of the dark sector in Horava-Lifshitz
  gravity
  Inclusion of $f(R)$ term in the action of Horava-Lifshitz quantum gravity
with projectability but without detailed balance condition is investigated,
where $R$ denotes the 3-spatial dimensional Ricci scalar. Conditions for the
spin-0 graviton to be free of ghosts and instability are studied. The
requirement that the theory reduce to general relativity in the IR makes the
scalar mode unstable in the Minkowski background but stable in the de Sitter.
It is remarkable that the dark sector, dark matter and dark energy, of the
universe has a naturally geometric origin in such a setup. Bouncing universes
can also be constructed. Scalar perturbations in the FRW backgrounds with
non-zero curvature are presented.
