Comment on “Strong coupling in extended Hořava–Lifshitz gravity” [Phys. Lett. B 685 (2010) 197

D Blas,O Pujolàs,S Sibiryakov

doi:10.1016/j.physletb.2010.03.073

Abstract

We show that, contrary to the claim made in arXiv:0911.1299, the extended Hořava gravity model proposed in arXiv:0909.3525 does not suffer from a strong coupling problem. By studying the observational constraints on the model we determine the bounds on the scale of the ultraviolet modification for which the proposal yields a phenomenologically viable, renormalizable and weakly coupled model of quantum gravity.

Highlights

We show that, contrary to the claim made in arXiv:0911.1299, the extended Hořava gravity model proposed in arXiv:0909.3525 does not suffer from a strong coupling problem
The consistency of the model presented in [3] has been recently questioned in [8], where it is claimed that the model suffers from the same kind of strong coupling problem as the previous versions of Hořava’s proposal [6, 7]
We follow [2] and, unlike the case of general relativity (GR), consider this foliation structure as physical. This means that the group of invariance of the theory is not the full group of 4-dimensional diffeomorphisms, but only its subgroup consisting of foliation-preserving transformations x → x(t, x), t → t(t)

Summary

Review of extended Hořava gravity

We start by describing briefly the model [3]. We consider the Arnowitt–Deser–Misner (ADM) decomposition for the metric, ds2 = (N 2 − NiN i)dt2 − 2Nidxidt − γijdxidxj. This action describes a scalar-tensor theory of gravity invariant under 4-dimensional diffeomorphisms and the symmetry (10). The first line in (12) contains all the terms with up to two derivatives acting on uμ and the metric; it describes the low-energy physics of the model. Note that this low-energy action is similar to a special case of the Einstein-aether theory (see [9] for a recent review). Besides the low-energy part, the full action of the model contains the terms with higher derivatives which we do not write explicitly These terms arise from the second and third lines in the potential (7).

The result has the schematic form

Observational bounds on the UV scale