Add at least 3 degrees of freedom beyond the 2 of the

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Unformatted text preview: t 3 degrees of freedom beyond the 2 of the massless graviton. With regard to the cosmological constant problem, there is the possibility of a technically natural explanation. The deformation parameter is m, the graviton mass, and GR should be restored as m ! 0. The force mediated by a massive graviton has a Yukawa profile $rÀ1 eÀmr , which drops off from that of a massless graviton at distances r * 1=m, so one 674 Kurt Hinterbichler: Theoretical aspects of massive gravity hopes to explain the acceleration of the Universe without dark energy by choosing the graviton mass to be of the order of the Hubble constant m $ H . Of course, this does not eliminate the small cosmological constant, which reappears as the ratio m=MP . But there is now hope that this is a technically natural choice, because deformation by a mass term breaks the gauge symmetry of GR, which is restored in the limit m ! 0. As we will see, a small m is indeed protected from quantum corrections (although there are other issues that prevent this, at our current stage of understanding, from being a completely satisfactory realization of a technically natural cosmological constant). There are also interesting lessons to be learned regarding the continuity of physical predictions. The addition of a mass term is a brutality upon the structure of GR and does not go unpunished. Various pathologies appear, which are representative of common pathologies associated with any infrared modification of gravity. These include strong classical nonlinearities, ghostlike instabilities, and a very low cutoff, or region of trustability, for the resulting quantum effective theory. In short, modifying the infrared often messes up the UV. New mechanisms also come into play, because the extra degrees of freedom carried by the massive graviton must somehow decouple themselves as m ! 0 to restore the physics of GR. The study of the massless limit leads to the discovery of the Vainshtein mechanism, by which these extra degrees of freedom hide themselves at short distances using nonlinearities. This mechanism has already proven useful for model builders who have long-range scalars, such as moduli from the extra dimensions of string theory, that they want to shield from local experiments that would otherwise rule them out. C. History and outline The possibility of a graviton mass has been studied off and on since 1939, when Fierz and Pauli (1939) first wrote the action describing a free massive graviton. Following this, not much occurred until the early 1970s, when there was a flurry of renewed interest in quantum field theory. The linear theory coupled to a source was studied by van Dam and Veltman (1970) and Zakharov (1970) (vDVZ), who discovered the curious fact that the theory makes predictions different from those of linear GR even in the limit as the graviton mass goes to zero. For example, massive gravity in the m ! 0 limit gives a prediction for light bending that is off by 25% from the GR predictio...
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