Does Cosmic No-Hair Conjecture in Brane Scenarios follow from General   Relativity?
  In this paper we examine the Cosmic No-Hair Conjecture (CNHC) in brane world 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 to be made on the quadratic correction term and there is a restriction on the non-local term. It is shown by examples with realistic fluid models that strong and weak energy conditions are sufficient for CNHC in brane world. 
Subenoy Chakraborty and Ujjal Debnath