Bianchi type II brane-world cosmologies $(\mathcal{U}>~0)$

The asymptotic properties of the Bianchi type II cosmological model in the brane-world scenario are investigated. The matter content is assumed to be a combination of a perfect fluid and a minimally coupled scalar field that is restricted to the brane. The isotropic brane-world solution is determined to represent the initial singularity in all brane-world cosmologies. Additionally, it is shown that it is the kinetic energy of the scalar field which dominates the initial dynamics in these brane-world cosmologies. It is important to note that the dynamics of these brane-world cosmologies is not necessarily asymptotic to general relativistic cosmologies to the future in the case of a zero four-dimensional cosmological constant.