  Using some simple toy models, we explore the nature of the brane-bulk
interaction for cosmological models with a large extra dimension. We are in
particular interested in understanding the role of the bulk gravitons, which
from the point of view of an observer on the brane will appear to generate
dissipation and nonlocality, effects which cannot be incorporated into an
effective (3+1)-dimensional Lagrangian field theoretic description. We
explicitly work out the dynamics of several discrete systems consisting of a
finite number of degrees of freedom on the boundary coupled to a
(1+1)-dimensional field theory subject to a variety of wave equations. Systems
both with and without time translation invariance are considered and moving
boundaries are discussed as well. The models considered contain all the
qualitative feature of quantized linearized cosmological perturbations for a
Randall-Sundrum universe having an arbitrary expansion history, with the sole
exception of gravitational gauge invariance, which will be treated in a later
paper.
