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

We study graviton propagations of scalar, vector, and tensor modes in the deformed Hořava-Lifshitz gravity (λR-model) without projectability condition. The quadratic Lagrangian is invariant under diffeomorphism only for λ=1 case, which contradicts to the fact that λ is irrelevant to a consistent Hamiltonian approach to the λR-model. In this case, as far as scalar propagations are concerned, there is no essential difference between deformed Hořava-Lifshitz gravity (λR-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 λ=1, the vDVZ discontinuity is absent in the massless limit of Lorentz-violating mass terms by considering external source terms.