# Are there Spin-2 bosons other than graviton?

## Main Question or Discussion Point

Are there Spin-2 bosons other than graviton? Does QFT allow for this?

Spin-1 bosons not only includes photons, but W Z bosons and gluons

could there be spin-2 bosons that have mass or have other types of charges?

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bapowell
The spin 2 excitation is the gauge boson associated with diffeomorphism (coordinate) invariance, much as the spin 1 excitation is associated with U(1) symmetry. In field theory, massless gauge bosons can be given a mass by breaking the symmetry under which they are charged. One could therefore generate a massive graviton by breaking diffeomorphism invariance.

The spin 2 excitation is the gauge boson associated with diffeomorphism (coordinate) invariance, much as the spin 1 excitation is associated with U(1) symmetry. In field theory, massless gauge bosons can be given a mass by breaking the symmetry under which they are charged. One could therefore generate a massive graviton by breaking diffeomorphism invariance.
What are the implications of breaking diffeomorphism invariance and generating massive gravitons?

bapowell
If gravitons are massive, then GR would need to be modified. There has been a bit of work on these ideas, termed massive gravity. For example, in linearized (weak) massive gravity, the Newton gravitational potential $\propto 1/r$ of the massless theory exhibits a Yukawa behavior, $\propto e^{-r}/r$. The DGP brane model also predicts massive gravitons, but I have not studied these theories closely.

If gravitons are massive, then GR would need to be modified. There has been a bit of work on these ideas, termed massive gravity. For example, in linearized (weak) massive gravity, the Newton gravitational potential $\propto 1/r$ of the massless theory exhibits a Yukawa behavior, $\propto e^{-r}/r$. The DGP brane model also predicts massive gravitons, but I have not studied these theories closely.
couldn't you have both massless gravitons and massive spin-2 bosons?

It can be shown that the unique fundamental spin-2 particle is the graviton. I believe that pertains to the massless graviton; I'd be surprised if the theorem did not apply to massive gravitons but I haven't looked into it. However, I will point out that there is nothing wrong with composite particles with spin-2 (composites of more elementary, less-than-spin-2 particles).

tom.stoer
It can be shown that the unique fundamental spin-2 particle is the graviton.
That is interesting.

Usually in gauge theories you can modify the underlying group structure and generate different spin-1 gauge bosons (photon, gluon, W, Z, ...). Now you say that this is different for gravity, that there is exactly one fundametal structure i.e. GR with diff. inv. or (which is equivalent) Poincare gauge symmetry and that it is not possible to modify this theory or to "add" a new structure coming with similar but not identical spin-2 gauge bosons.

Do you have a reference or a name for that theorem?

Demystifier
Gold Member
Do you have a reference or a name for that theorem?
There are many papers on it. See e.g. Refs. [6-12] in
http://xxx.lanl.gov/abs/gr-qc/9901057
By the way, the theorem refers to massless spin-2 particles only.

There are many papers on it. See e.g. Refs. [6-12] in
http://xxx.lanl.gov/abs/gr-qc/9901057
By the way, the theorem refers to massless spin-2 particles only.
Is there any theorem that includes massive spin-2 bosons?

Could there be phenomena, for example MOND or DM, or dark energy, that could be explained in terms of either massive spin-2 bosons or composite spin-2 fields/particles?

http://prl.aps.org/abstract/PRL/v94/i18/e181102

Phys. Rev. Lett. 94, 181102 (2005) [4 pages]
Massive Graviton as a Testable Cold-Dark-Matter Candidate
Abstract
References
Citing Articles (43)

S. L. Dubovsky1,3, P. G. Tinyakov2,3, and I. I. Tkachev1,3
1Department of Physics, CERN Theory Division, CH-1211 Geneva 23, Switzerland
2Service de Physique Théorique, Université Libre de Bruxelles, CP225, boulevard du Triomphe, B-1050 Bruxelles, Belgium
3Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia

Received 19 November 2004; published 9 May 2005

We construct a consistent model of gravity where the tensor graviton mode is massive, while linearized equations for scalar and vector metric perturbations are not modified. The Friedmann equation acquires an extra dark-energy component leading to accelerated expansion. The mass of the graviton can be as large as ∼(1015  cm)-1, being constrained by the pulsar timing measurements. We argue that nonrelativistic gravitational waves can comprise the cold dark matter and may be detected by the future gravitational wave searches.

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To answer the original question: spin 2 bosons are attractive only, the other forces mediated by spin 1 bosons both attract and repel. So I don't believe there are any other spin 2 bosons.

To answer the original question: spin 2 bosons are attractive only, the other forces mediated by spin 1 bosons both attract and repel. So I don't believe there are any other spin 2 bosons.
I'm not sure about the spin-2 boson being attractive only. Mathematically if you had a region of negative energy density it should emit bosons which repel regions of positive energy density.

I'm not sure about the spin-2 boson being attractive only. Mathematically if you had a region of negative energy density it should emit bosons which repel regions of positive energy density.
Oh and there are claims that matter-antimatter antigravitates: http://arXiv.org/pdf/1103.4937

That's not well founded. Antimatter has positive energy density since the annihilation releases 2mc^2 of energy.

The closest thing resembling negative energy density that I know of is the particle that falls into a black hole in Hawking radiation and reduces the gravity of the black hole. Assuming that it really happens, the spin-2 bosons from that particle should repel, no?