Generate the operator 12 h2 which 3 corrects

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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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