Modified F(R) Hořava-Lifshitz gravity: A way to accelerating FRW cosmology

Classical and Quantum Gravity (Impact Factor: 3.17). 08/2010; 27(18):185021. DOI: 10.1088/0264-9381/27/18/185021
Source: arXiv


We propose a general approach for the construction of modified gravity which is invariant under foliation-preserving diffeomorphisms. Special attention is paid to the formulation of a modified F(R) Hořava–Lifshitz gravity (FRHL), whose Hamiltonian structure is studied. It is demonstrated that the spatially flat FRW equations of FRHL are consistent with the constraint equations. The analysis of de Sitter solutions for several versions of FRHL indicates that the unification of the early-time inflation with the late-time acceleration is possible. It is shown that a special choice of parameters for FRHL leads to the same spatially flat FRW equations as in the case of the traditional F(R)-gravity. Finally, an essentially most general modified Hořava–Lifshitz gravity is proposed, motivated by its fully diffeomorphism-invariant counterpart, with the restriction that the action does not contain derivatives higher than the second order with respect to the time coordinate.

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    • "For a review, see [31]. Generalized Hořava-Lifshitz gravitational theories were proposed and analyzed in [32] [33] [34] [35]. Proposals of covariant alternatives to Hořava-Lifshitz gravity were presented in [36] [37] and their Hamiltonian structure was studied in [38] [39]. "
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    • "Since a violation of Lorentz invariance has never been observed, one could try to argue that CRG is a more natural modification of GR than the explicitly Lorentz noninvariant ones, in particular HL gravity and its generalizations (see e.g. [12] [13] [14] [15]). On the other hand Lorentz invariance could equally well be broken explicitly at very high energies as long as it is somehow restored at sufficiently low energies. "
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    • "Thus, this particular form of f (R) gravity does not change the pure gravity part in FRW space-time. In contrast to the other version of f (R) HL gravity [15], the vacuum solution does not admit de-Sitter solution. As we see from Eq. (19), similar to the standard HL gravity, many novel terms are proportional to the spatial curvature. "
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