**Unformatted text preview: **uperluminality is a
sign that the theory cannot be UV completed by a standard
local Lorentz invariant theory (Adams et al., 2006), though
this remains controversial and others have argued that this is
not a problem (Babichev, Mukhanov, and Vikman, 2008). In
addition, the analysis of Nicolis, Rattazzi, and Trincherini
(2008) was for pure Galileons only, and the scalar-tensor
couplings of the massive gravity Lagrangian can potentially
change the story. These issues have been studied within
massive gravity by Gruzinov (2011) and de Rham,
Gabadadze, and Tolley (2011b).
IX. BRANE WORLDS AND THE RESONANCE GRAVITON So far, we have stuck to the effective ﬁeld theorist’s
philosophy. We have explored the possibility of a massive
graviton by simply writing down the most general mass term
a graviton can have, remaining agnostic as to its origin.
However, it is important to ask whether such a mass term
has a top down construction or embedding into a wider
structure, one which would determine the coefﬁcients of all
the various interactions. This goes back to the question of
whether it is possible to UV complete (or UV extend) the
effective ﬁeld theory of a massive graviton.
One way in which a massive graviton naturally arises is
from higher dimensions. We now study one of these higher
dimensional scenarios, the DGP brane world model, showing
how massive gravitons emerge in a 4d description.
The DGP model (Dvali, Gabadadze, and Porrati, 2000a) is
an extra-dimensional model which has spawned a great deal
of interest [see the many papers citing Dvali, Gabadadze, and
Porrati (2000a)]. It provides another, more novel realization
of a graviton mass. Unlike the Kaluza-Klein scenario, in DGP
the extra dimensions can be inﬁnite in extent, although there
must be a brane on which to conﬁne standard model matter
[see (Gabadadze (2003) for discussion on large extra dimensions]. By integrating out the extra dimensions, we can write
an effective 4d action for this scenario which contains a
momentum dependent mass term for the graviton. This provides an example of a graviton resonance, i.e., a continuum of
massive gravitons.
Another model that has received a great deal of attention is
the Randall-Sundrum brane world (Randall and Sundrum,
1999), in which there is a brane ﬂoating in large warped extra
dimensions. This model is not as interesting from the point of
view of massive gravity at low energies, since the 4d spectrum is similar to ordinary Kaluza-Klein theory, containing
ordinary Einstein gravity as a zero mode, and then massive
gravitons as higher Kaluza-Klein modes. See Langlois
(2002), Brax, van de Bruck, and Davis (2004), Kiritsis
(2005), and Maartens and Koyama (2010) for other reviews
on aspects of brane world gravity and cosmology.
A. The DGP action FIG. 2. Regimes for massive gravity with cutoff Ã3 ¼ ðMP m Þ
(i.e., M is the solar mass and m is taken to be the Hubble scale) and
some values within the Solar System. The values are much more
reasona...

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