Lessons from the decoupling limit of Hořava gravity

Abstract

We consider the so-called "healthy" extension of Hořava gravity in the limit where the Stuckelberg field decouples from the graviton. We verify the alleged strong coupling problem in this limit, under the assumption that no large dimensionless parameters are put in by hand. This follows from the fact that the dispersion relation for the Stuckelberg field does not have the desired z = 3 anisotropic scaling in the UV. To get the desired scaling and avoid strong coupling one has to introduce a low scale of Lorentz violation and retain some coupling between the graviton and the Stuckelberg field. We also make use of the foliation preserving symmetry to show how the Stuckelberg field couples to some violation of energy conservation. We source the Stuckelberg field using a point particle with a slowly varying mass and show that two such particles feel a constant attractive force. In this particular example, we see no Vainshtein effect, and violations of the Equivalence Principle. The latter is probably generic to other types of source and could potentially be used to place lower bounds on the scale of Lorentz violation. * ppxik1@nottingham.ac.uk

Stability of spin-0 graviton and strong coupling in Horava-Lifshitz theory of gravity

“…Such a study also helps us to clarify some differences regarding to the strength of strong couplings, obtained recently in [25][26][27]31]. In addition, the treatment in this section can be applied to the HL theory both with and without the projectability condition.…”

“…Despite all of these attractive features, the theory plagues with two serious problems: the instability of the Minkowski background [4,11,[20][21][22], and the strong coupling [23][24][25][26][27]. To solve these problems, various modifications were proposed [28,29].…”

“…However, a price to pay in such a setup is the enormous number of independent coupling constants. It can be shown that only the sixth-order derivative terms in the potential are more than 60 [27]. It should be also noted that giving up the projectability condition often causes the theory to suffer the inconsistence problem [36].…”

U(1) symmetry and elimination of spin-0 gravitons in Horava-Lifshitz gravity without the projectability condition

“…Abandoning the general diffeomorphisms, on the other hand, gives rise to a proliferation of independently coupling constants [2,15], which could potentially limit the prediction powers of the theory. In particular, only the sixth-order spatial derivative terms are more than 60 [16]. To reduce the number of the independent coupling constants, two conditions were introduced, the projectibility and detailed balance [2].…”

“…Despite of all the above remarkable features, the theory (with these two conditions) is plagued with several problems [3], including the instability, ghost [2,21], and strong coupling [16,22]. However, all of them are closely related to the existence of the spin-0 gravitons [3].…”