Brane-bulk energy exchange and the Universe as a global attractor
  The assumption that our Universe is close to a late time fixed point of the equations of cosmology, leads to a modification of the latter to include energy exchange between the matter and the "dark energy". The brane-world scenario provides a natural set-up for such energy exchange and is analyzed in detail. The role of brane-bulk energy exchange and of an induced gravity term on a single braneworld of negative tension and vanishing effective cosmological constant is studied. It is shown that for the physically interesting cases of dust and radiation a unique global attractor which can realize our present universe (accelerating and $0<\Omega_{m0}<1$) exists for a wide range of the parameters of the model. For $\Omega_{m0}=0.3$, independently of the other parameters, the model predicts that the equation of state for the dark energy today is $w_{DE,0}=-1.4$, while $\Omega_{m0}=0.03$ leads to $w_{DE,0}=-1.03$. In addition, during its evolution, $w_{DE}$ crosses the $w_{DE}=-1$ line to smaller values. 
Theodore N. Tomaras