Gravitational Interactions in a General Multibrane Model

The gravitational interactions of the four-dimensional effective theory describing a general $N$-brane model in five dimensions without radion stabilization are analyzed. Both uncompactified and orbifolded models are considered. The parameter space is constrained by requiring that there be no ghost modes in the theory, and that the Eddington parameterized post-Newtonian parameter $\gamma$ be consistent with observations. We show that we must reside on the brane on which the warp factor is maximized. The resultant theory contains $N-1$ radion modes in a nonlinear sigma model, with the target space being a subset of hyperbolic space. Imposing observational constraints on the relative strengths of gravitational interactions of dark and visible matter shows that at least 99.8% of the dark matter must live on our brane in this model.