Cosmological dynamics on the brane - art. no. 084023

In Randall-Sundrum-type brane-world cosmologies, the dynamical equations on the three-brane differ from the general relativity equations by terms that carry the effects of embedding and of the free gravitational field in the five-dimensional bulk. Instead of starting from an ansatz for the metric, w e derive the covariant nonlinear dynamical equations for the gravitational and matter fields on the brane, and then linearize to find the perturbation equations on the brane. The local energy-momentum corrections are signific ant only at very high energies. The imprint on the brane of the nonlocal gr avitational field in the bulk is more subtle, and we provide a careful deco mposition of this effect into nonlocal energy density, flux and anisotropic stress. The nonlocal energy density determines the tidal acceleration in t he off-brane direction, and can oppose singularity formation via the genera lized Raychaudhuri equation. Unlike the nonlocal energy density and flux, t he nonlocal anisotropic stress is not determined by an evolution equation o n the brane, reflecting the fact that brane observers cannot in general mak e predictions from initial data. In particular, isotropy of the cosmic micr owave background may no longer guarantee a Friedmann geometry. Adiabatic de nsity perturbations are coupled to perturbations in the nonlocal bulk field , and in general the system is not closed on the brane. But on super Hubble scales, density perturbations satisfy a decoupled third-order equation, an d can be evaluated by brane observers. Tensor perturbations on the brane ar e suppressed by local bulk effects during inflation, while nonlocal effects can serve as a source or a sink. Vorticity on the brane decays as in gener al relativity, but nonlocal bulk effects can source the gravito-magnetic fi eld, so that vector perturbations can be generated in the absence of vortic ity.