DOE OSTI2011
In this paper, we investigate three important issues: stability, ghost, and strong coupling, in the Horava-Melby-Thompson setup of the Horava-Lifshitz theory with {lambda}{ne}1, generalized recently by da Silva. We first develop the general linear scalar perturbations of the Friedmann-Robertson-Walker (FRW) universe with arbitrary spatial curvature and find that an immediate by-product of the setup is that, in all the inflationary models described by a scalar field, the FRW universe is necessarily flat. Applying them to the case of the Minkowski background, we find that it is stable, and, similar to the case {lambda}=1, the spin-0 graviton is eliminated. The vector perturbations vanish identically in the Minkowski background. Thus, similar to general relativity, a free gravitational field in this setup is completely described by a spin-2 massless graviton, even with {lambda}{ne}1. We also study the ghost problem in the FRW background and find explicitly the ghost-free conditions. To study the strong coupling problem, we consider two different kinds of spacetimes, all with the presence of matter: one is cosmological, and the other is static. We find that the coupling becomes strong for a process with energy higher than M{sub pl}|c{sub {psi}|}{sup 5/2} in the flat FRW background and M{sub pl}|c{sub {psi}|}{sup 3} in a static weak gravitational field, where |c{sub {psi}|{identical_to}}|(1-{lambda})/(3{lambda}-1)|{sup 1/2}.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗