Note about equivalence of F(R) and scalar-tensor Horava-Lifshitz gravities

In this paper we study the relation between F(R) and scalar-tensor Horava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance which is a characteristic property of Horava-Lifshitz gravities corresponding scalar-tensor theory that is related to F(R) Horava-Lifshitz gravity by specific Weyl transformation has a more complicated form than in the case of the full diffeomorphism invariant F(R) theory of gravity and its scalar-tensor formulation. We also show that in the low energy limit this theory reduces to the relativistic scalar-tensor theory of gravity.