Lorentz-violating graviton masses: getting around ghosts, low strong coupling scale and VDVZ discontinuity

TL;DR

The paper proposes a Lorentz-violating deformation of gravity with a graviton mass term set to evade ghosts and the VDVZ discontinuity. Through a tensor–vector–scalar analysis and a Stückelberg high-energy check, it shows that with $m_0=0$ the theory has a mass gap $\sim m$, relativistic tensor modes, and vector/scalar sectors with canonical normalisations implying a strong-coupling scale $\sim (m M_{Pl})^{1/2}$. Importantly, in the massless limit the interactions reproduce GR, demonstrating no VDVZ discontinuity, and the positivity conditions on the masses prevent ghosts and tachyons. This work suggests a healthy Higgs phase of gravity with Lorentz violation that can modify infrared gravity without ghosts or VDVZ, potentially enabling consistent IR modifications.

Abstract

A theory with the action combining the Einstein--Hilbert term and graviton mass terms violating Lorentz invariance is considered at linearized level about Minkowskian background. It is shown that with one of the masses set equal to zero, the theory has the following properties: (i) there is a gap of order $m$ in the spectrum, where $m$ is the graviton mass scale; (ii) the dispersion relations at ${\bf p}^2 \gg m^2$ are $ω^2 \propto {\bf p}^2$, the spectrum of tensor modes being relativistic, while other modes having unconventional maximum velocity; (iii) the VDVZ discontinuity is absent; (iv) the strong coupling scale is $(mM_{Pl})^{1/2}$. The latter two properties are in sharp contrast to the Lorentz-invariant gravity with the Pauli--Fierz mass term.