  We consider the evolution of a bulk scalar field in anti-de Sitter (AdS)
spacetime linearly coupled to a scalar field on a de Sitter boundary brane. We
present results of a spectral analysis of the system, and find that the model
can exhibit both bound and continuum resonant modes. We find that zero, one, or
two bound states may exist, depending upon the masses of the brane and bulk
fields relative to the Hubble length and the AdS curvature scale and the
coupling strength. In all cases, we find a critical coupling above which there
exists a tachyonic bound state. We show how the 5-dimensional spectral results
can be interpreted in terms of a 4-dimensional effective theory for the bound
states. We find excellent agreement between our analytic results and the
results of a new numerical code developed to model the evolution of bulk fields
coupled to degrees of freedom on a moving brane. This code can be used to model
the behaviour of braneworld cosmological perturbations in scenarios for which
no analytic results are known.
