Dynamics of Scalar field in a Brane World
  We study the dynamics of a scalar field in the brane cosmology. We assume that a scalar field is confined in our 4-dimensional world. As for the potential of the scalar field, we discuss three typical models: (1) a power-law potential, (2) an inverse-power-law potential, and (3) an exponential potential. We show that the behavior of the scalar field is very different from a conventional cosmology when the energy density square term is dominated. 
Shuntaro Mizuno, Kei-ichi Maeda, Kohta Yamamoto