Note About Equivalence of F(R) and Scalar Tensor Horava-Lifshitz Gravities

TL;DR

This paper explores the relationship between F(R) gravity and scalar tensor Horava-Lifshitz gravity, highlighting differences due to broken invariance and showing the low-energy limit converges to relativistic scalar tensor gravity.

Contribution

It clarifies the connection and differences between F(R) and scalar tensor Horava-Lifshitz gravities, especially under broken diffeomorphism invariance.

Findings

Scalar tensor Horava-Lifshitz gravity is more complex than F(R) gravity due to broken invariance.

In the low-energy limit, the theory reduces to relativistic scalar tensor gravity.

The study elucidates the flow from Horava-Lifshitz to relativistic gravity regimes.

Abstract

In this note we study the relation between F(R) and scalar tensor Horava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance corresponding scalar tensor theory has more complicated form than in case of the full diffeomorphism invariant F(R) theory of gravity. We also show that in the low energy limit this theory flows to the relativistic scalar tensor theory of gravity.