Strong coupling in Horava gravity (0905.2579v2)

Abstract: By studying perturbations about the vacuum, we show that Horava gravity suffers from two different strong coupling problems, extending all the way into the deep infra-red. The first of these is associated with the principle of detailed balance and explains why solutions to General Relativity are typically not recovered in models that preserve this structure. The second of these occurs even without detailed balance and is associated with the breaking of diffeomorphism invariance, required for anisotropic scaling in the UV. Since there is a reduced symmetry group there are additional degrees of freedom, which need not decouple in the infra-red. Indeed, we use the Stuckelberg trick to show that one of these extra modes become strongly coupled as the parameters approach their desired infra-red fixed point. Whilst we can evade the first strong coupling problem by breaking detailed balance, we cannot avoid the second, whatever the form of the potential. Therefore the original Horava model, and its "phenomenologically viable" extensions do not have a perturbative General Relativity limit at any scale. Experiments which confirm the perturbative gravitational wave prediction of General Relativity, such as the cumulative shift of the periastron time of binary pulsars, will presumably rule out the theory.

• The paper demonstrates that Hořava gravity inherently suffers from strong coupling problems that invalidate its linearized perturbation approach.
• The analysis shows that applying detailed balance limits the theory’s parameters and prevents the recovery of General Relativity in the infrared limit.
• The study reveals that the extra degrees of freedom from broken diffeomorphism invariance lead to issues akin to those in massive gravity models.

Strong Coupling in Hořava Gravity: A Critical Analysis

The paper "Strong coupling in Hořava gravity" by Christos Charmousis, Gustavo Niz, Antonio Padilla, and Paul M. Saffin critically examines Hořava gravity, a quantum gravity theory known for its anisotropic scaling properties and potential renormalizability at high energy. Hořava gravity aims to recover General Relativity (GR) in the infrared (IR) limit through relevant deformations, while explicitly breaking Lorentz invariance in the ultraviolet (UV) regime. This theory has gained attention due to its unique approach to dealing with the UV divergences inherent in quantum field theories.

Key Findings

1. Strong Coupling Problems: The authors demonstrate that Hořava gravity suffers from strong coupling problems regardless of the principle of detailed balance being applied or broken. The paper of perturbations around the vacuum shows that the breakdown of linearized theory occurs due to strong coupling, which is intrinsic to the structure of the theory.
2. Detailed Balance Principle: Detailed balance, borrowed from critical phenomena, limits the number of parameters in Hořava gravity by relating the potential of the theory to a lower-dimensional "superpotential." While it provides organizational elegance, the authors argue that it renders the theory incapable of recovering GR in the IR. The strong coupling issue persists in all scales, as the Planck length diverges in the detailed balance limit.
3. Broken Diffeomorphism Invariance: Without full diffeomorphism invariance, prominently present in GR, Hořava gravity possesses additional propagating degrees of freedom, which become strongly coupled as the parameters move towards the IR fixed point. This is akin to the scenario in Pauli-Fierz massive gravity, where the longitudinal scalar mode becomes strongly coupled as the mass approaches zero. The Stuckelberg trick is used to reveal this strong coupling behavior.
4. Infrared Limit and General Relativity Recovery: Despite modifying detailed balance to mitigate the first strong coupling issue, the theory does not reach a perturbative GR limit at any scale due to the irreducible presence of extra degrees of freedom. Even for models dubbed "phenomenologically viable," the inability to decouple these additional degrees signals a strong coupling problem.

Implications and Future Considerations

The finding that Hořava gravity exhibits severe strong coupling challenges its viability as a model for quantum gravity. The inability to recover GR at any perturbative scale, combined with potential violations of observational confirmations of GR, such as gravitational wave predictions and binary pulsar timing, suggests that the theory faces significant hurdles.

Theoretically, this work indicates that breaking Lorentz invariance and relying on restricted diffeomorphism invariance complicates the theory’s framework, introducing problematic degrees of freedom. Practically, since the theory’s predictions diverge from observed phenomena in scenarios like strong gravitational fields, Hořava gravity lacks fundamental consistency with existing experimental data.

Future investigations may explore alternate ways to incorporate Lorentz invariance recovery or examine modified principles that do not introduce additional degrees of freedom so as to circumvent the highlighted issues. Developing methods to handle UV divergences without compromising diffeomorphism invariance could also be an area of focus.

Conclusively, while the paper focuses on the theoretical drawbacks of Hořava gravity, it opens avenues for dialogue on potentially refining quantum gravity theories through a more nuanced understanding of fundamental symmetries.