Bianchi IX Brane-world Cosmologies

We shall investigate the asymptotic properties of the Bianchi type IX cosmological model in the Brane-world scenario. The matter content is assumed to be a combination of a perfect fluid and a minimimally coupled scalar field that is restricted to the Brane. A detailed qualitative analysis of the Bianchi type IX braneworld containing a scalar field having an exponential potential is undertaken. It is found that the Brane-Robertson Walker solution is a local source for the expanding Bianchi IX models, and if $k^2<2$ the expanding Bianchi IX models asymptote to the power-law inflationary solution. The only other local sink is the contracting Brane-Robertson Walker solution. An analysis of the Bianchi IX models with a scalar field with a general potential is discussed, and it is shown that in the case of expanding models, for physical scalar field potentials close to the initial singularity, the scalar field is effectively massless, and the solution is approximated by the Brane-Robertson Walker model.