U(1) Invariant F(R) Hořava―Lifshitz gravity

• Published in: The European physical journal. C, Particles and fields Vol. 71; no. 7; pp. 1 - 16
• Main Authors: KLUSON, J, NOJIRI, S, ODINTSOV, S. D, SAEZ-GOMEZ, D
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01-07-2011
• Subjects: Consistency; Gravitation; Gravitons; Invariants; Mathematical analysis; Polarization; Scalars; Spectrum analysis
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-011-1690-6

This paper is devoted to the study of various aspects of projectable F(R) Horava-Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and unstable flat-space solution. In this case, the problem of scalar graviton does not appear because flat space is not vacuum state. Generalizing the U(1) HL theory proposed in arXiv:1007.2410, we formulate U(1) extension of scalar theory and of F(R) Horava-Lifshitz gravity. The Hamiltonian approach for such the theory is developed in full detail. It is demonstrated that its Hamiltonian structure is the same as for the non-relativistic covariant HL gravity. The spectrum analysis performed around the flat background indicates the consistency of the theory because it contains a graviton with only transverse polarization. Finally, we analyze the spatially flat FRW equations for U(1) invariant F(R) Horava-Lifshitz gravity.