Inflation on a single brane - exact solutions
  Algorithms are developed for generating a class of exact braneworld cosmologies, where a self-interacting scalar field is confined to a positive-tension brane embedded in a bulk containing a negative cosmological constant. It is assumed that the five-dimensional Planck scale exceeds the brane tension but is smaller than the four-dimensional Planck mass. It is shown that the field equations can be expressed as a first-order system. A number of solutions to the equations of motion are found. The potential resulting in the perfect fluid model is identified. 
Rachael M. Hawkins and James E. Lidsey