Fluctuating brane in a dilatonic bulk

We consider a cosmological brane moving in a static five-dimensional bulk spacetime endowed with a scalar field whose potential is exponential. After studying various cosmological behaviours for the homogeneous background, we investigate the fluctuations of the brane that leave spacetime unaffected. A single mode embodies these fluctuations and obeys a wave equation which we study for bouncing and ever-expanding branes.