Consistent Hořava gravity without extra modes and equivalent to general relativity at the linearized level

Abstract

We consider a Hořava theory that has a consistent structure of constraints and propagates two physical degrees of freedom. The Lagrangian includes the terms of Blas, Pujolàs, and Sibiryakov. The theory can be obtained from the general Horava's formulation by setting λ = 1/3. This value of λ is protected in the quantum formulation of the theory by the presence of a constraint. The theory has two second-class constraints that are absent for other values of λ. They remove the extra scalar mode. There is no strong-coupling problem in this theory since there is no extra mode. We perform explicit computations on a model that put together a z = 1 term and the IR effective action. We also show that the lowest-order perturbative version of the IR effective theory has a dynamics identical to the one of linearized general relativity. Therefore, this theory is smoothly recovered at the deepest IR without discontinuities in the physical degrees of freedom.

Solutions with throats in Hořava gravity with cosmological constant

“…We have found no barriers that would avoid the two-way movement of physical particles between the internal points of the two sides of the solutions (excluding the asymptotic singularity at one side). We also comment that the complete nonprojectable Hořava theory at λ = 1/3 has no ghosts (it has no extra degrees at all) [6] and for λ = 1/3 one may require λ > 1 in the linearized theory to safe the extra degree from becoming a ghost [2]. The solutions we have found here are valid for any λ.…”

“…[2,3,4]. But when λ = 1/3 the theory acquires two extra second-class constraints that eliminate the extra scalar degree, thus at λ = 1/3 the theory propagates exactly the same degrees of freedom of GR [6]. Interestingly, at λ = 1/3 the full kinetic term (2.4) acquires a conformal covariance [1], but in general the terms in the potential break this conformal symmetry.…”

“…The decoupling of this extra mode at low energies faces with the so-called strong coupling problem [10,11,12,13]. However, at the conformal point of the kinetic term, λ = 1/3, the theory propagates exactly the same modes of GR as a consequence of additional second-class constraints that arise at this point [6] (see also [14]). This is a outstanding feature, since there is no need of any decoupling mechanism and there are no discontinuity issues at low energies.…”

“…This is a outstanding feature, since there is no need of any decoupling mechanism and there are no discontinuity issues at low energies. This suggests that theory can be smoothly connected to GR [7,6]. Because of this we consider the λ = 1/3 case of the nonprojectable theory as a interesting model among the various proposals known for quantum gravity.…”

“…In this sense the Hořava proposal [1] of having an ultraviolet completion of GR with a preferred foliation of space-time has been studied widely. Among the several versions that have been proposed, the complete nonprojectable version [1,2] exhibits a good behavior in what concerns to the structure of the field equations and constraints [2,3,4,5,6]. For this version most of the analysis has been done outside the conformal point of the kinetic term, which holds at the value λ = 1/3 of its corresponding coupling constant.…”