Graviton Mass or Cosmological Constant?

TL;DR

The paper analyzes whether a local Lorentz-invariant quadratic mass term can yield a massive graviton on 4D Minkowski space. It shows that the Pauli-Fierz term, while ghost-free at linear order, induces instabilities upon nonlinear completion; alternative non-Pauli-Fierz terms carry ghosts unless nonlinear background rearrangements are invoked, which then destroy the Yukawa-type propagation on flat space. The authors argue that a truly consistent flat-space massive graviton is attainable primarily in theories with extra dimensions, where an infinite tower of Kaluza-Klein gravitons (or nonlocal 4D descriptions) preserves stability and yields an effective graviton mass without local 4D ghosts. They discuss DGP-like models and infinite-volume extra dimensions as viable routes, contrasting them with 4D local theories that either become curved or nonlocal. The work highlights the central tension between mass terms, background stability, and the role of extra dimensions in obtaining a physically acceptable massive graviton.

Abstract

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of describing a massive graviton on flat space. We show that for all local Lorentz-invariant mass terms Minkowski space is unstable. We start with the Pauli-Fierz (PF) term that is the only local mass term with no ghosts in the linearized approximation. We show that nonlinear completions of the PF Lagrangian give rise to instability of Minkowski space. We continue with the mass terms that are not of a PF type. Although these models are known to have ghosts in the linearized approximations, nonlinear interactions can lead to background change due to which the ghosts are eliminated. In the latter case, however, the graviton perturbations on the new background are not massive. We argue that a consistent theory of a massive graviton on flat space can be formulated in theories with extra dimensions. They require an infinite number of fields or non-local description from a 4D point of view.