Massive graviton propagation of the deformed Hořava-Lifshitz gravity without projectability condition

Abstract

We study graviton propagations of scalar, vector, and tensor modes in the deformed Hořava-Lifshitz gravity ($\lambda R$-model) without projectability condition. The quadratic Lagrangian is invariant under diffeomorphism only for $\lambda =1$ case, which contradicts to the fact that $\lambda$ is irrelevant to a consistent Hamiltonian approach to the $\lambda R$ model. In this case, as far as scalar propagations are concerned, there is no essential difference between deformed Hořava-Lifshitz gravity ($\lambda R$-model) and general relativity. This implies that there are two degrees of freedom for a massless graviton without Hořava scalar, and five degrees of freedom appear for a massive graviton when introducing Lorentz-violating and Fierz-Pauli mass terms. Finally, it is shown that for $\lambda =1$, the vDVZ discontinuity is absent in the massless limit of Lorentz-violating mass terms by considering external source terms.

21 pages, no figure, version to appear in PLB

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Cited by in corpus (5)

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• Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de Sitter space
• Minimal-supersymmetric extended inflation field in Horava-Lifshitz gravity
• Considerations on the Graviton Excitation Modes of Horava-Lifshitz Gravity