Does the cosmic no-hair conjecture in brane scenarios follow from general relativity?

In this paper we examine the cosmic no-hair conjecture (CNHC) in braneworld scenarios. For the validity of this conjecture, in addition to the strong- and weak-energy conditions for the matter field, a similar type of assumption is made on the quadratic correction term and there is a restriction on the non-local term. It is shown using examples with realistic fluid models that strong- and weak-energy conditions are sufficient for the CNHC in braneworld scenarios.