An alternative approach for general covariant Hořava–Lifshitz gravity and matter coupling

Abstract

Recently, Hořava and Melby-Thompson proposed in [3] a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduce the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of λ to be λ = 1 as claimed in [3]. However, the spin-0 graviton is eliminated even for general λ.PACS numbers: 98.80.Qc;

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

“…As a matter of fact, it is exactly its presence that leads the enlarged symmetry to exist not only in the case with any coupling constant λ [11], but also in the case without the projectability condition, as one can see from Eq. (10).…”

“…Applied to cosmology, it results in various remarkable features and has attracted a great deal of attention [3]. In particular, high order spatial derivative terms can give rise to a bouncing universe [4,5]; the anisotropic scaling solves the horizon problem and leads to scale-invariant perturbations without inflation [6,7]; the lack of the local Hamiltonian constraint leads to "dark matter as an integration constant" [8]; the dark sector can have its purely geometric origins [9]; and the inclusion of a U(1) symmetry (with the projectability condition) [10,11] not only eliminates the spin-0 gravitons but also leads to a flat universe [12].…”

“…This was initially done in the special case λ = 1, and soon generalized to the case with any λ [11], where λ is a coupling constant defined below. Although the spin-0 gravitons are also eliminated in the general case, the strong coupling problem raises again [12].…”

“…However, it can be solved by the Blas-Pujolas-Sibiryakov (BPS) mechanism [15], in which a new energy scale M * is introduced, so that M * < Λ ω , where M * denotes the suppression energy of high order derivative terms of the theory, and Λ ω the would-be strong coupling energy scale [25]. Note that in [10,11] the projectability condition was assumed. In this paper, we shall study the case without it, and our goals are twofold: (i) Extend the symmetry (3) to the case without the projectability condition, so that the spin-0 gravitons are eliminated.…”

Non-relativistic holography from Hořava gravity

“…The consistent expansion of the metric can be determined by first considering the case of C µ = c 2 b t δ t µ , similar to the warm-up example. In this frame the metric can be decomposed in the ADM form 4 25) where…”