0 20 40 71 v 1 2 2 A pr 2 00 2 Asymptotic states in brane cosmology with a nonlocal anisotropic stress

We investigate the dynamics of a Bianchi I brane Universe in the presence of a nonlocal anisotropic stress Pµν proportional to a " dark energy " U. Using this ansatz for the case U > 0 we prove that if a matter on a brane satisfies the equation of state p = (γ − 1)ρ with γ ≤ 4/3 then all such models isotropize. For γ > 4/3 anisotropic future asymptotic states are found. We also describe the past asymptotic regimes for this model.