Abstract
In this paper we study the relation between $F(R)$ and scalar-tensor Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance which is a characteristic property of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravities corresponding scalar-tensor theory that is related to $F(R)$ Ho\ifmmode \check{r}\else \v{r}\fi{}ava-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.
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