Horava-Lifshitz gravity: detailed balance revisited

TL;DR

This paper critically revisits the detailed balance principle in Horava-Lifshitz gravity, showing that removing projectability significantly reduces couplings and highlights a large cosmological constant issue, with potential implications for vacuum energy cancellation.

Contribution

It demonstrates that abandoning projectability enhances the effectiveness of detailed balance in reducing couplings and uncovers a significant cosmological constant problem.

Findings

Removing projectability reduces couplings by an order of magnitude.

Detailed balance imposes a large cosmological constant constraint.

Potential for cancelation between bare and vacuum energy contributions.

Abstract

We attempt a critical reconsideration of "detailed balance" as a principle that can be used to restrict the proliferation of couplings in Horava-Lifshitz gravity. We re-examine 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 under-appreciated 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 cancelation between the bare cosmological constant and the (still poorly understood) vacuum energy contribution.