# Graviton mass or cosmological constant?

## 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 4D Lorentz-invariant mass terms Minkowski space is unstable. The instability can develop in a time scale that is many orders of magnitude shorter than the inverse graviton mass. 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 in 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 nonlocal description from a 4D point of view.

- Authors:

- Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, New York, 10003 (United States)

- Publication Date:

- OSTI Identifier:
- 20774528

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.72.124007; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; CONSERVATION LAWS; COSMOLOGICAL CONSTANT; COSMOLOGY; DISTURBANCES; GRAVITONS; INSTABILITY; LAGRANGIAN FUNCTION; LORENTZ INVARIANCE; MINKOWSKI SPACE; NONLINEAR PROBLEMS; QUANTUM GRAVITY; REST MASS; SPACE-TIME

### Citation Formats

```
Gabadadze, Gregory, and Gruzinov, Andrei.
```*Graviton mass or cosmological constant?*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.124007.

```
Gabadadze, Gregory, & Gruzinov, Andrei.
```*Graviton mass or cosmological constant?*. United States. doi:10.1103/PhysRevD.72.124007.

```
Gabadadze, Gregory, and Gruzinov, Andrei. Thu .
"Graviton mass or cosmological constant?". United States.
doi:10.1103/PhysRevD.72.124007.
```

```
@article{osti_20774528,
```

title = {Graviton mass or cosmological constant?},

author = {Gabadadze, Gregory and Gruzinov, Andrei},

abstractNote = {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 4D Lorentz-invariant mass terms Minkowski space is unstable. The instability can develop in a time scale that is many orders of magnitude shorter than the inverse graviton mass. 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 in 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 nonlocal description from a 4D point of view.},

doi = {10.1103/PhysRevD.72.124007},

journal = {Physical Review. D, Particles Fields},

number = 12,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}