On the infrared limit of Hořava’s gravity with the global Hamiltonian constraint

We show that Hořava’s theory of gravitation with the global Hamiltonian constraint does not reproduce General Relativity in the infrared domain. There is one extra propagating degree of freedom, besides those two associated with massless graviton, which does not decouple. Introduction. Recently, Hořava proposed power-counting renormalizable higher-derivative theory of gravitation where the full diffeomorphism invariance is broken down to the foliation-preserving diffeomorphism [1]. Because of the reduced symmetry, the ghost states usually associated with the higher time derivatives in General Relativity (GR), are removed, and thus the theory is unitary. A vital question is whether Hořava’s theory of gravitation has an infrared limit consistent with observations. Since the observational success of GR is largelly based on the its full diffeomorphism invariance, it is clear that any theory with reduced diffeomorphism invariance will deviate from GR both in the ultraviolet and infrared regimes. From the purely phenomenological point of view, it is important to understand whether this deviation in the infrared regime can be made consistent with observations. In [2] it has been pointed out that the scalar polarization of graviton does not decouple in Hořava’s theory. Also, it has been shown in [3] that in Hořava’s theory with local Hamiltonian constraint the Poisson algebra is not closed. From this perspectives it seems vital to retain ”projectability condition” which generates less restrictive global Hamiltonian constraint [5]. In this paper we consider the infrared limit of Hořava’s theory with the global Hamiltonian constraint. By applying Dirac’s constraint analysis, we show that there is one extra propagating degree of freedom, besides those two associated with massless graviton. Therefore, Hořava’s theory of gravitation does not reproduce General Realativity in the infrared regime. Dirac’s constraint analysis. In the infrared limit, Hořava’s theory is described by the following action1: SHorava = ∫