Graviton Mass or Cosmological Constant?

TL;DR

The paper investigates the stability of Minkowski space with massive graviton theories, showing local Lorentz-invariant mass terms lead to instability, and proposes extra-dimensional theories as a consistent alternative.

Contribution

It demonstrates that local Lorentz-invariant mass terms cause Minkowski instability and suggests extra-dimensional models as a consistent framework for massive gravitons.

Findings

Minkowski space is unstable with local Lorentz-invariant mass terms.

Nonlinear effects can eliminate ghosts but remove graviton mass.

Extra-dimensional theories provide a consistent massive graviton framework.

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.