In this paper we study the relation between $F(R)$ and scalar-tensor Hořava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance which is a characteristic property of Hořava-Lifshitz gravities corresponding scalar-tensor theory that is related to $F(R)$ Hořava-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.

• Received 4 September 2011

DOI:https://doi.org/10.1103/PhysRevD.84.104014