Abstract
In this paper, we consider two different issues, stability and strong coupling, which have been raised recently in the newly proposed Horava-Lifshitz theory of quantum gravity with the projectability condition. We find that all the scalar modes are stable in the de Sitter background, due to two different kinds of effects, one from high-order derivatives of the spacetime curvature and the other from the exponential expansion of the de Sitter space. Combining these effects properly, one can make the instability found in the Minkowski background never appear even for small-scale modes, provided that the IR limit is sufficiently close to the relativistic fixed point. At the fixed point, all the modes become stabilized. We also show that the instability of Minkowski spacetime can be cured by introducing mass to the spin-0 graviton. The strong coupling problem is investigated following the effective field theory approach, and we find that it cannot be cured by the Blas-Pujolas-Sibiryakov mechanism, initially designed for the case without the projectability condition, but might be circumvented by the Vainshtein mechanism, due to the nonlinear effects. In fact, we construct a class of exact solutions, and show explicitly that they reduce smoothly to the de Sitter spacetime in the relativistic limit.
2 More- Received 24 September 2010
DOI:https://doi.org/10.1103/PhysRevD.83.044025
© 2011 American Physical Society