**Unformatted text preview: **e Ã3 . If this is true, it is
important that the Ã3 theory is ghost free beyond the decoupling limit.
It should also be noted that massive gravitons already exist
in nature, in the form of tensor mesons which carry spin 2.
There is a nonet of them, which at low energies can be
described in chiral perturbation theory as a multiplet of
massive gravitons (Chow and Rey, 1998). Here we know
that these states ﬁnd a UV completion in QCD, where they
are simply excited states of bound quarks.
In this review we focused on theories with a vacuum that
preserves Lorentz invariance, but there is a whole new world
that opens up when one allows for Lorentz violation. There
exist theories that explicitly break Lorentz invariance, and
theories such as the ghost condensate (Arkani-Hamed et al.,
2004) which have Lorentz invariance spontaneously broken
(Arkani-Hamed et al., 2005) by some non-Lorentz invariant
background. In the former case, a systematic study of the
possible mass terms and their degrees of freedom, generalizing the Fierz-Pauli analysis to the case where the mass term
preserves only rotation invariance, is performed by Dubovsky
(2004). For examples of the latter case, see Berezhiani et al.
(2007) and Blas, Deffayet, and Garriga (2007). See also
Rubakov (2004), Gabadadze and Grisa (2005), Rubakov
and Tinyakov (2008), Bebronne (2009b), and Mironov
et al. (2010) for reviews.
There is still much to be learned about massive gravitons
on curved spaces and cosmologies. For instance, does a
generalization exist of the higher cutoff Ã3 theory around
curved backgrounds? Is there a consistent fully interacting
theory of the partially massless theories on de Sitter space?
Are there consistent theories with cosmological backgrounds,
and, in particular, can they nonlinearly realize the screening
of a large bare cosmological constant while maintaining
consistency with Solar System constraints?
Finally, a topic worthy of a separate review is the observable signatures that would be characteristic of a massive
graviton. What would be the signatures of a cosmological
constant screened by a graviton mass? For some examples of
various proposed signatures, see Dubovsky, Tinyakov, and
Rev. Mod. Phys., Vol. 84, No. 2, April–June 2012 707 Tkachev (2005), Bebronne (2009a), Bessada and Miranda
(2009a, 2009b), Dubovsky et al. (2010), and Wyman
(2011). We end this review by quoting the tantalizing current
experimental limits on the mass of the graviton (under some
hypotheses, of course) m & 7 Â 10À32 eV (Goldhaber and
Nieto, 2010; Nakamura et al., 2010), about an order of
magnitude above the Hubble scale, the value needed to
theoretically explain the cosmological constant naturalness
problem.
ACKNOWLEDGMENTS The author would like to thank Claudia de Rham, Gregory
Gabadadze, Lam Hui, Justin Khoury, Janna Levin, Alberto
Nicolis, and Claire Zukowski for discussions and comments
on the manuscript, and Mark Trodden for discussions, comments, and for encouraging the writing of this...

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