Expected from dimensionally reducing a noncompact fth

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Unformatted text preview: oni constant, and the length scale r0 is r0  terms, so we should have < 1. Additionally, there is the constraint that the spectral function (9.53) should be positive definite, so that there are no ghosts. This puts a lower bound ! 0 (Dvali, 2006). It turns out that degravitation can be made to work only for < 1=2 (Dvali, Hofmann, and Khoury, 2007). DGP corresponds to ¼ 1=2, and so it just barely fails to degravitate, but by extending the DGP idea to higher codimension (Kiritsis, Tetradis, and Tomaras, 2001; de Rham, 2008; Hassan, Hofmann, and von Strauss, 2011) or to multibrane cascading DGP models (de Rham et al., 2008; de Rham, 2009; de Rham, Khoury, and Tolley, 2010), < 1=2 can be achieved and degravitation made to work (de Rham et al., 2008). Some N -body simulations of degravitation and DGP have been done by Chan and Scoccimarro (2009), Khoury and Wyman (2009), and Schmidt (2009). 1 M2 ¼ 43 : m 2M 5 (9.57) The potential interpolates between 4d $ 1=r and 5d $ 1=r2 behavior at the scale r0 , 8 > 2 2M þ M 2 r1 ½ À 1 þ lnðrr ފ þ OðrÞ; r ( r0 ; < 3 M 4r 32 M 0 0 4 4 V ð rÞ ¼ 2 M > 3 2 2 þ Oð 13 Þ; : 3 M 4 r r ) r0 : r 5 (9.58) Physically, we think of gravity as being confined to the brane out to a distance $r0 , at which point it starts to weaken and leak off the brane, becoming five dimensional. This is the behavior that is morally responsible for the self-accelerated solutions seen in DGP (Deffayet, Dvali, and Gabadadze, 2002). It has been suggested that corrections to the Newtonian potential for r ( r0 may be observable in lunar laser ranging experiments (Dvali, Gruzinov, and Zaldarriaga, 2003; Lue and Starkman, 2003). The resonance massive graviton can also be generalized away from DGP, by replacing the mass term with an arbitrary function of the Laplacian (Gabadadze and Shifman, 2004; Dvali, 2006; Dvali, Hofmann, and Khoury, 2007), m2 ! m2 ðhÞ: (9.59) [See Dvali, Pujolas, and Redi (2008) for even further generalizations.] At large distances, where we want modifications to occur, the mass term has a leading Taylor expansion m2 ðhÞ ¼ L2ð À1Þ h ; (9.60) with L being a length scale and being a constant. In order to modify Newtonian dynamics at large scales, @ ( 1=L, the mass term should dominate over the two derivative kinetic Rev. Mod. Phys., Vol. 84, No. 2, April–June 2012 Massive gravity remains an active research area, one which may provide a viable solution to the cosmological constant naturalness problem. As seen, many interesting effects arise from the naive addition of a hard mass term to Einstein gravity. There is a well-defined effective field theory with a protected hierarchy between the cutoff and the graviton mass, and a screening mechanism which nonlinearly hides the new degrees of freedom and restores continuity with GR in the massless limit. A massive graviton can screen a large cosmological constant, and a stable theory of massive gravity with a small protected mass offers a s...
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