Linearized Lorentz-violating gravity and discriminant locus in the moduli space of mass terms

Abstract

We analyze the pattern of normal modes in linearized Lorentz-violating massive gravity over the five-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 the vanishing of the coefficient in front of ω2 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 . When the Lorentz invariance is broken, these two kinds of bifurcations become 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.