Eur. Phys. J. C (2011) 71: 1690
https://doi.org/10.1140/epjc/s10052-011-1690-6

Regular Article - Theoretical Physics

U(1) Invariant Hořava–Lifshitz gravity

¹ Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic
² Department of Physics, and Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, 464-8602, Japan
³ Instituciò Catalana de Recerca i Estudis Avançats (ICREA), Passeig Luis Companys 23, 08010, Barcelona, Spain
⁴ TSPU, Tomsk, Russia
⁵ Instituto de Ciencias del Espacio, ICE (CSIC-IEEC), Campus UAB, Facultat de Ciències, Torre C5-Parell-2a pl, 08193, Bellaterra (Barcelona), Spain

^* e-mail: klu@physics.muni.cz

Received: 6 May 2011
Revised: 11 May 2011
Published online: 7 July 2011

Abstract

This paper is devoted to the study of various aspects of projectable F(R) Hořava–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) Hořava–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) Hořava–Lifshitz gravity.