Hořava-Lifshitz gravity: Detailed balance revisited
Abstract
We attempt a critical reconsideration of ``detailed balance'' as a principle that can be used to restrict the proliferation of couplings in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity. We reexamine the shortcomings that have been usually associated with it in the literature and we argue that easy remedies can be found for all of them within the framework of detailed balance, and that the most persistent of them are actually related to projectability. We show that, once projectability is abandoned, detailed balance reduces the number of independent couplings by roughly an order of magnitude and imposes only one restriction that constitutes a phenomenological concern: the size of the (bare) cosmological constant is unacceptably large. Remarkably, this restriction (which is present in the projectable version as well) has been so far underappreciated in the literature. Optimists might prefer to interpret it as a potential blessing in disguise, as it allows one to entertain the idea of a miraculous cancellation between the bare cosmological constant and the (still poorly understood) vacuum energy contribution.