Inflation in Bianchi models and the cosmic no hair theorem in a brane world

The cosmic no hair theorem is studied in anisotropic brane worlds. Assuming anisotropic Bianchi models with an inflaton field it is shown that, during slow-roll inflation, anisotropy in all Bianchi models except a Bianchi type-IX universe washes out. Brane worlds admit both exponential and power law inflation. We consider here only exponential expansion of the universe. It is found that isotropization occurs much faster in a brane world than in the general theory of relativity.