Reheating the Universe in Braneworld Cosmological Models with bulk-brane   energy transfer
  The emergence of the cosmological composition (the reheating era) after the inflationary period is analyzed in the framework of the braneworld models, in which our Universe is a three-brane embedded in a five-dimensional bulk, by assuming the possibility of the brane-bulk energy exchange. The inflaton field is assumed to decay into normal matter only, while the dark matter is injected into the brane from the bulk. To describe the reheating process we adopt a phenomenological approach, by describing the decay of the inflaton field by a friction term proportional to the energy density of the field. After the radiation dominated epoch the model reduces to the standard four dimensional cosmological model. The modified field equations are analyzed analytically and numerically in both the extra-dimensions dominate reheating phase (when the quadratic terms in energy density dominate the dynamics), and in the general case. The evolution profiles of the matter, of the scalar field and of the scale factor of the universe are obtained for different values of the parameters of the model, and of the equations of state of the normal and dark matter, respectively. The equation describing the time evolution of the ratio of the energy density of the dark and of the normal matter is also obtained. The ratio depends on the rate of the energy flow between the bulk and the brane. The observational constraint of an approximately constant ratio of the dark and of the baryonic matter requires that the dark matter must be non-relativistic (cold). The model predicts a reheating temperature of the order of $3\times 10^6$ GeV, a brane tension of the order of $10^{25}$ GeV$^4$, and the obtained composition of the universe is consistent with the observational data. 
T. Harko, W. F. Choi, K. C. Wong, K. S. Cheng