Modified F(R) HoavaLifshitz 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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    ABSTRACT: We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable -- a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.
    Physical Review D 11/2013; 89(6). DOI:10.1103/PhysRevD.89.064043 · 4.64 Impact Factor
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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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    ABSTRACT: In order to explore some general features of modified theories of gravity which involve higher derivatives and spontaneous Lorentz and/or diffeomorphism symmetry breaking, we study the recently proposed new version of covariant renormalizable gravity (CRG). CRG attains power-counting renormalizability via higher derivatives and introduction of a constrained scalar field and spontaneous symmetry breaking. We obtain an Arnowitt-Deser-Misner representation of the CRG action in four-dimensional spacetime with respect to a foliation of spacetime adapted to the constrained scalar field. The resulting action is analyzed by using Hamiltonian formalism. We discover that CRG contains two extra degrees of freedom. One of them carries negative energy (a ghost) and it will destabilize the theory due to its interactions. This result is in contrast with the original paper [Phys. Lett. B 701, 117 (2011), arXiv:1104.4286 [hep-th]], where it was concluded that the theory is free of ghosts and renormalizable when we analyze fluctuations on the flat background.
    Physical review D: Particles and fields 08/2012; 87(6). DOI:10.1103/PhysRevD.87.064032 · 4.86 Impact Factor
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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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    ABSTRACT: We discuss the cosmology of recently proposed Hořava–Lifshitz f(R)f(R) gravity. In particular, we derive the modified Hubble equation that reduces to the standard HL gravity case in appropriate limit. We show how the bounce solutions in this theory are modified due to nonlinear effect of f(R)f(R) gravity. We also show that in principle, the Universe in this set-up can show cyclic behavior.
    Physics Letters B 05/2012; 711(2):147–152. DOI:10.1016/j.physletb.2012.03.080 · 6.13 Impact Factor
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