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In the Horava-Lifshitz theory of quantum gravity, two conditions---detailed balance and projectability---are usually assumed. The breaking of projectability simplifies the theory, but it leads to serious problems with the theory. The breaking of detailed balance leads to a more complicated form of the theory, but it appears to resolve some of the problems. Sotiriou, Visser and Weinfurtner formulated the most general theory of Horava-Lifshitz type without detailed balance. We compute the linear scalar perturbations of the FRW model in this form of HL theory. We show that the higher-order curvature terms in the action lead to a gravitational effective anisotropic stress on small scales. Specializing to a Minkowski background, we study the spin-0 scalar mode of the graviton, using a gauge-invariant analysis, and find that it is stable in both the infrared and ultraviolet regimes for 02/3. However, in this parameter range the scalar mode is a ghost.
Wang et al. (2010) studied this question.