Stability of spin-0 graviton and strong coupling in Horava-Lifshitz theory of gravity

Abstract

In this paper, we consider two different issues, stability and strong coupling, raised lately in the newly-proposed Horava-Lifshitz (HL) theory of quantum gravity with projectability condition. We find that all the scalar modes are stable in the de Sitter background, due to two different kinds of effects, one from high-order derivatives of the spacetime curvature, and the other from the exponential expansion of the de Sitter space. Combining these effects properly, one can make the instability found in the Minkowski background never appear even for small-scale modes, provided that the IR limit is sufficiently closed to the relativistic fixed point. At the fixed point, all the modes become stabilized. We also show that the instability of Minkowski spacetime can be cured by introducing mass to the spin-0 graviton. The strong coupling problem is investigated following the effective field theory approach, and found that it cannot be cured by the Blas-Pujolas-Sibiryakov mechanism, initially designed for the case without projectability condition, but might be circumvented by the Vainshtein mechanism, due to the non-linear effects. In fact, we construct a class of exact solutions, and show explicitly that it reduces smoothly to the de Sitter spacetime in the relativistic limit.PACS numbers: 98.80.Cq; 98.80.Bp

Hořava gravity at a Lifshitz point: A progress report

“…It is also interesting to note that the de Sitter spacetime in this minimal theory is stable [106,107]. See also a recent study of the issue in a closed FLRW universe [108].…”

“…In addition, the BPS mechanism cannot be applied to the minimal theory presented in the last subsection, because the condition M * < Λ ω , together with the one that instability cannot occur within the age of the universe, requires fine-tuning |λ − 1| < 10 −24 , as shown explicitly in [106]. However, in the current setup (with any λ), the Minkowski spacetime is stable, so such a fine-tuning does not exist.…”

“…In the projectable case without the local U(1) symmetry presented in Section II.A, the minimal theory, the main issues are instability [92,104,105], and strong coupling of the spin-0 graviton [106,109]. The perturbation analysis shows that the Minkowski spacetime is not stable due to the presence of the spin-0 graviton [92,104,105], which questions the viability of the theory (although the de Sitter spacetime is [106,107]). To solve the strong coupling problem, one way is to borrow the well-known Vainshtein mechanism [113].…”

“…In addition, this minimal theory still suffers the strong coupling problem [106,109], so the power-counting analysis presented above becomes invalid. It must be noted that this does not necessarily imply the loss of predictability: if the theory is renormalizable, all coefficients of infinite number of nonlinear terms can be written in terms of finite parameters in the action, as several wellknown theories with strong coupling (e.g., [110]) indicate.…”

Oscillating Bianchi IX universe in Hořava-Lifshitz gravity

“…In order to recover general relativity (or the Lorentz invariance) in our world, one expects that the constant converges to unity in the infrared (IR) limit in the renormalization flow. Although it has been argued that there exist some fundamental problems in HL gravity [5][6][7][8][9][10][11][12][13][14][15][16], some extensions are proposed to remedy these difficulties [10,[17][18][19]. It is an intriguing issue whether or not HL gravity can be a complete theory of quantum gravity.…”