Cosmological perturbations in Horava-Lifshitz theory without detailed
  balance
  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 $0 \le \xi \le 2/3$. However,
in this parameter range the scalar mode is a ghost.
