The first half of this talk reviews the basic construction and some
known cosmological implications of a renormalizable theory of
gravitation called Horava-Lishitz gravity. In particular, I will
explain that (i) the anisotropic scaling with the dynamical critical
exponent z=3 renders a field theory of gravity renormalizable, that
(ii) the same anisotropic scaling solves the horizon problem and leads
to scale-invariant cosmological perturbations even without inflation
and that (iii) the infrared instability of the so-called projectable
version of the theory can be tamed under a certain condition. We then
propose a possible solution to the cosmological flatness problem, in
which we assume that the initial condition of the Universe is set by a
small instanton respecting the same anisotropic scaling.