The Shape of Gravity

Abstract

In a nontrivial background geometry with extra dimensions, gravitational effects will depend on the shape of the Kaluza-Klein excitations of the graviton. We investigate a consistent scenario of this type with two positive tension three-branes separated in a five-dimensional Anti-de Sitter geometry. The graviton is localized on the ``Planck'' brane, while a gapless continuum of additional gravity eigenmodes probe the {\it infinitely} large fifth dimension. Despite the background five-dimensional geometry, an observer confined to either brane sees gravity as essentially four-dimensional up to a position-dependent strong coupling scale, no matter where the brane is located. We apply this scenario to generate the TeV scale as a hierarchically suppressed mass scale. Arbitrarily light gravitational modes appear in this scenario, but with suppressed couplings. Real emission of these modes is observable at future colliders; the effects are similar to those produced by {\it six} large toroidal dimensions.

Figures (1)

• Figure 1: Schematic view of the Kaluza-Klein gravity modes. The x-axis is the fifth dimension. The left/right vertical lines represent the Planck/TeV branes. The "volcano" potential rises then falls off rapidly away from the Planck brane. Plotted are the squared amplitudes of two KK gravity modes relative to the graviton zero mode. The heavy $m>>1$ TeV mode takes its asymptotic (oscillating) form at the TeV brane, the other mode exhibits the characteristic behavior for $m<<1$ TeV. Very light modes with $m<10^{-4}$ eV would appear as flat lines, since they track the zero mode.