Linearized Lorentz-Violating Gravity and Discriminant Locus in the Moduli Space of Mass Terms

TL;DR

This paper studies the behavior of normal modes in linearized Lorentz-violating massive gravity, identifying conditions for ghost-free models and the absence of the DVZ discontinuity within the moduli space of mass parameters.

Contribution

It reveals how Lorentz violation allows for ghost-free massive gravity models without the DVZ discontinuity in the linearized regime.

Findings

Ghost-free theories occur at bifurcation points where ghosts exit the spectrum.

DVZ discontinuities arise at different bifurcations where the propagator coefficient vanishes.

Lorentz violation decouples the conditions for ghost-freeness and the DVZ discontinuity.

Abstract

We analyze the pattern of normal modes in linearized Lorentz-violating massive gravity over the 5-dimensional moduli space of mass terms. Ghost-free theories arise at bifurcation points when the ghosts get out of the spectrum of propagating particles due to vanishing of the coefficient in front of \omega^2 in the propagator. Similarly, the van Dam-Veltman-Zakharov (DVZ) discontinuities in the Newton law arise at another type of bifurcations, when the coefficient vanishes in front of \vec k^2. When the Lorentz invariance is broken, these two kinds of bifurcations get independent and one can easily find a ghost-free model without the DVZ discontinuity in the moduli space, at least, in the quadratic (linearized) approximation.