The case in gr there is no intermediate regime where

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ry makes no observable predictions within its range of validity. Kurt Hinterbichler: Theoretical aspects of massive gravity so there is no hope of finding the leading quantum corrections. Finally, the radius rQ is the same as the radius rghost , where the ghost mass drops below the cutoff, so it is consistent to ignore the ghost since it lies beyond the reach of the quantum effective theory. The various regions are shown in Fig. 1. Note that in the decoupling limit we are working in, the Schwarzschild radius (and the radii associated to all scales larger than Ã5 ) are sent to zero, while the scale r $ 1=m where Yukawa suppression takes hold is sent to infinity. VIII. THE Ã3 THEORY We have seen that the theory (5.1) containing only the linear graviton mass term has some undesirable features, including a ghost instability and quantum corrections that become important before classical nonlinearities can restore continuity with GR. In this section, we consider the higher order potential terms in Eq. (5.3) and ask whether they can alleviate these problems. It turns out that there is a special choice of potential that cures all these problems, at least in the decoupling limit. This choice also has the advantage of raising the cutoff. With only the Fierz-Pauli mass term, the strong coupling cutoff was set by the cubic scalar self-coupling ^ [email protected] Þ3 =Ã5 . The cutoff Ã5 ¼ ðMP m4 Þ1=5 is very low, and 5 as we see generically any interaction term will have this cutoff. But by choosing this special tuning of the higher order interactions, we end up raising the cutoff to the higher scale Ã3 ¼ ðMP m2 Þ1=3 . Arkani-Hamed, Georgi, and Schwartz (2003) already recognized that if the scalar self-interactions could be eliminated, the cutoff would be raised to Ã3 . This was studied more fully by Creminelli et al. (2005), where the cancellation was worked through and it was (mistakenly) concluded that ghosts would be unavoidable once the cutoff was raised. Motivated by constructions of massive gravity with auxiliary extra dimensions (Gabadadze, 2009; de Rham, 2010; de Rham and Gabadadze, 2010b), this was revisited by de Rham and Gabadadze (2010a) and de Rham, Gabadadze, and Tolley (2010), where the decoupling limit Lagrangian was calculated explicitly and was seen to be ghost free. The full theory was shown to be ghost free by Hassan and Rosen (2011a, 2011c). Looking back at the scales (7.5), the term suppressed by the smallest scale is the cubic scalar term, which is suppressed by the scale Ã5 ¼ ðMP m4 Þ1=5 , ^ [email protected] Þ3 : MP m4 (8.1) The next highest scale is Ã4 ¼ ðMP m Þ , carried by a quartic scalar interaction, and a cubic term with a single vector and two scalars, 3 1=4 $ ^ [email protected] Þ4 ; 2 MP m6 $ ^ ^ @[email protected] Þ2 : MP m 3 Rev. Mod. Phys., Vol. 84, No. 2, April–June 2012 The next highest is a quintic scalar, and so on. The only terms which carry a scale less than Ã3 ¼ ðMP m2 Þ1=3 are terms with ^ only scalars [email protected] Þn , and terms with one...
View Full Document

This document was uploaded on 09/28/2013.

Ask a homework question - tutors are online