Uv completion takes over should cure the ghost

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Unformatted text preview: 1=2 5=2 (7.18) >M :M Ã5 r3=2 ; r ( rV : P At distances much below the Vainshtein radius, the ghost mass (7.16) becomes very small, and the ghost starts to Kurt Hinterbichler: Theoretical aspects of massive gravity mediate a long-range force. Usually a scalar field mediates an attractive force, but due to the ghost’s wrong sign kinetic term, the force mediated by it is repulsive. In fact, it cancels the attractive force due to the longitudinal mode, the force responsible for the vDVZ discontinuity, and so general relativity is restored inside the Vainshtein radius. We now see this more explicitly. Following Deffayet and Rombouts (2005), some field redefinitions can be done on the scalar action (7.10), and the result is an action schematically of the form ~ L ¼ Àð@Þ2 þ ð@ c Þ2 þ Ã5=2 c 3=2 þ 5 þ 1~ T MP 1 c T: MP ~ Here  is the healthy longitudinal mode, c is the ghost mode, ^ ~ and the original scalar can be found from  ¼  À c . Both are coupled gravitationally to the stress tensor. Note that the self-interactions appear in these variables as a peculiar nonanalytic c 3=2 term (we can also see that the ghost mass ~ around a background h c i will be Ã5=2 =h c i1=2 ). The  field 5 ~ $ ðM=MP Þð1=rÞ everywhere, is free and has the profile  mediating an attractive force. The c field, however, has two competing terms, which become comparable at the Vainshtein radius. The linear term dominates at radii smaller than the Vainshtein radius, so c $ ðM=MP Þð1=rÞ for r ( rV . This profile generates a repulsive Coulomb force that exactly cancels the attractive ~ force mediated by , so in sum there are no extra forces beyond gravity in this region. [The leading correction to the profile is found by treating the c 3=2 term as a perturbation, c $ c 0 þ c ð1Þ þ Á Á Á , with c 0 $ ðM=MP Þð1=rÞ, plugging = in the equation of motion @2 c ð1Þ þ Ã5=2 c 10Þ2 ¼ 0 obtaining 5 ð 5=2 3=2 c ð1Þ $ ðM=MP Þ1=2 Ã5 r , in agreement with Eq. (7.18).] The funny nonlinear term dominates at radii larger than the Vainshtein radius, so c $ ðM=MP Þ2 1=Ã5 r6 for r ) rV , and 5 so the ghost profile is negligible in this region compared to ~ the  profile. Thus the ghost ceases to be active beyond the Vainshtein radius, and the longitudinal mode generates a fifth force. This is known as a screening mechanism, a mechanism for rendering a light scalar inactive at short distances through nonlinearities [see the Introduction and references in Hinterbichler and Khoury (2010) and Hinterbichler, Khoury, and Nastase (2010), and in a different context (Gabadadze and Iglesias, 2008)]. One can think of this as a kind of classical version of a weakly coupled UV completion via a Higgs. Above the Vainshtein radius (low energies), there is only the long distance scalar, which starts to become nonlinear (strongly coupled) around the Vainshtein radius, so one can think of this regime in terms of an effective field theory with cutoff o...
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This document was uploaded on 09/28/2013.

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