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

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.

12 pages,v2: references added

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Cited by in corpus (4)

• Thermal stability of a special class of black hole solutions in F(R) gravity
• Notes on diffeomorphisms symmetry of $f(R)$ gravity in the cosmological context
• Hořava-Lifshitz $F(\bar{R})$ theories and the Swampland
• Composite Nambu--Jona-Lasinio inflation near infrared fixed point of the Horava-Lifshitz theory