Asymptotic behavior of homogeneous cosmological models on the brane

In this work, we have studied the late-time behavior of initially expanding homogeneous cosmological models with a positive cosmological term in Randall-Sundrum brane-world type scenarios. The matter fields are confined in the three-brane, onto which the five-dimensional Weyl tensor has a nonvanishing projection. It is found that all Bianchi models (except IX) exponentially evolve toward the de Sitter solution while the Bianchi IX model also isotropizes but with a restriction on the cosmological parameter.