U(1) symmetry and elimination of spin-0 gravitons in Horava-Lifshitz gravity without the projectability condition

TL;DR

This paper demonstrates that extending gauge symmetries in Horava-Lifshitz gravity eliminates problematic spin-0 gravitons, resolving stability issues and reducing coupling constants, thus making the theory more consistent and predictive.

Contribution

The authors introduce a local U(1) symmetry extension in Horava-Lifshitz gravity without projectability, removing spin-0 gravitons and simplifying the theory's parameter space.

Findings

Spin-0 gravitons are eliminated by the U(1) extension.

Stability, ghost, and strong coupling issues are resolved.

Number of coupling constants reduced from over 70 to 15.

Abstract

In this paper, we show that the spin-0 gravitons appearing in Horava-Lifshitz gravity without the projectability condition can be eliminated by extending the gauge symmetries of the foliation-preserving diffeomorphisms to include a local U(1) symmetry. As a result, the problems of stability, ghost, strong coupling, and different speeds in the gravitational sector are automatically resolved. In addition, with the detailed balance condition softly breaking, the number of independent coupling constants can be significantly reduced (from more than 70 down to 15), while the theory is still UV complete and possesses a healthy IR limit, whereby the prediction powers of the theory are considerably improved. The strong coupling problem in the matter sector can be cured by introducing an energy scale $M_{*}$, so that $M_{*} < \Lambda_{\omega}$, where $M_{*}$ denotes the suppression energy of high order derivative terms, and $\Lambda_{\omega}$ the would-be strong coupling energy scale.