Can be made sense of as an effective eld theory valid

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Unformatted text preview: ense of as an effective field theory, valid only at energies below some ultraviolet cutoff scale Ã. In 2003, Arkani-Hamed, Georgi, and Schwartz (2003) brought to attention a method of restoring gauge invariance to massive gravity in a way that makes it very simple to see what the effective field theory properties are. They showed that massive gravity generically has a maximum UV cutoff of Ã5 ¼ ðMP m4 Þ1=5 . For Hubble scale graviton mass, this is a length scale ÃÀ1 $ 1011 km. This is a very small cutoff, 5 parametrically smaller than the Planck mass, and goes to zero as m ! 0. Around a massive source, the quantum effects become important at the radius rQ ¼ ðM=MPl Þ1=3 ð1=Ã5 Þ, which is parametrically larger than the Vainshtein radius at which nonlinearities enter. For the Sun, rQ $ 1024 km. Without finding a UV completion or some other resummation, there is no sense in which we can trust the solution inside this radius, and the usefulness of massive gravity is limited. In particular, since the whole nonlinear regime is below this radius, there is no hope to examine the continuity of physical quantities in m and explore the Vainshtein mechanism in a controlled way. On the other hand, it can be seen that the mass of the Boulware-Deser ghost drops below the cutoff only when r & rQ , so the ghost is not really in the effective theory at all and can be consistently excluded. Kurt Hinterbichler: Theoretical aspects of massive gravity Putting aside the issue of quantum corrections, there has been continued study of the Vainshtein mechanism in a purely classical context. It has been shown that classical nonlinearities do indeed restore continuity with GR in certain circumstances. In fact, the ghost degree of freedom can play an essential role in this, by providing a repulsive force in the nonlinear region to counteract the attractive force of the longitudinal scalar mode. By adding higher order graviton self-interactions with appropriately tuned coefficients, it is in fact possible to raise the UV cutoff of the theory to Ã3 ¼ ðMP m2 Þ1=3 , corresponding to roughly ÃÀ1 $ 103 km. In 2010, the complete action 3 of this theory in a certain decoupling limit was worked out by de Rham and Gabadadze (2010a), and they show that, remarkably, it is free of the Boulware-Deser ghost. Recently, it was shown that the complete theory is free of the BoulwareDeser ghost. This Ã3 theory is the best hope of realizing a useful and interesting massive gravity theory. The subject of massive gravity also naturally arises in extra-dimensional setups. In a Kaluza-Klein scenario such as GR in 5d compactified on a circle, the higher Kaluza-Klein modes are massive gravitons. Brane world setups such as the Dvali-Gabadadze-Porrati (DGP) model (Dvali, Gabadadze, and Porrati, 2000a) give more intricate gravitons with resonance masses. The study of such models has complemented the study of pure 4d massive gravity and has pointed toward new research directions....
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This document was uploaded on 09/28/2013.

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