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.

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- Théorie