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 parametrized 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.

Figure 1

An illustration of the model a) before and b) after gauge fixing. The bulk cosmological constants ${\Lambda }_n$, brane tensions ${\sigma }_n$, and metrics ${}^{n}g_{\alpha \beta }$ are labeled.

Figure 2

The behavior of the warp factor at a brane interface in the eight possible configurations. An increasing warp factor in a region has $P_n=+1$, while a decreasing warp factor has $P_n=-1$. In cases 2, 3, 6 and 7, the adjacent bulk cosmological constants can be equal. The horizontal axis in all plots is the $y$ coordinate.

Figure 3

A diagram of the warp factor between branes and the associated bulk cosmological constants (dashed). Branes are represented as vertical lines. The bulk cosmological constants are negative, while the warp factor lies between 0 and 1.

Figure 4

Diagram indicating how the branes are labeled in the construction of the orbifolded model. The orbifold symmetry identifies $y$ with $-y$, and we impose the periodicity condition of identifying $y$ with $y+2N-2$. To calculate the action, the model is broken up into $2(N-1)$ bulk regions ${\mathcal{R}}_n$, but regions ${\mathcal{R}}_n$ and ${\mathcal{R}}_{-n}$ coincide by the orbifold symmetry.