  This article reviews basic construction and cosmological implications of a
power-counting renormalizable theory of gravitation recently proposed by
Horava. We explain that (i) at low energy this theory does not exactly recover
general relativity but instead mimic general relativity plus dark matter; that
(ii) higher spatial curvature terms allow bouncing and cyclic universes as
regular solutions; and that (iii) the anisotropic scaling with the dynamical
critical exponent z=3 solves the horizon problem and leads to scale-invariant
cosmological perturbations even without inflation. We also comment on issues
related to an extra scalar degree of freedom called scalar graviton. In
particular, for spherically-symmetric, static, vacuum configurations we prove
non-perturbative continuity of the lambda->1+0 limit, where lambda is a
parameter in the kinetic action and general relativity has the value lambda=1.
We also derive the condition under which linear instability of the scalar
graviton does not show up.
