Brane-bulk energy exchange: a model with the present universe as a global attractor

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 < Ωm0 < 1) exists for a wide range of the parameters of the model. For Ωm0 = 0.3, independently of the other parameters, the model predicts that the equation of state for the dark energy today is wDE,0 = −1.4, while Ωm0 = 0.03 leads to wDE,0 = −1.03. In addition, during its evolution, wDE crosses the wDE = −1 line to smaller values.