Reheating the Universe in braneworld cosmological models with bulk–brane energytransfer

Abstract

The emergence of the cosmological composition (the reheating era) after the inflationaryperiod is analyzed in the framework of the braneworld models, in which our Universe is a3-brane embedded in a five-dimensional bulk, by assuming the possibility of brane–bulkenergy exchange. The inflaton field is assumed to decay into normal matter only, while thedark matter is injected into the brane from the bulk. To describe the reheating process weadopt a phenomenological approach, by describing the decay of the inflaton fieldusing a friction term proportional to the energy density of the field. After theradiation dominated epoch the model reduces to the standard four-dimensionalcosmological model. The modified field equations are analyzed analytically andnumerically in both the extra-dimension dominated reheating phase (when thequadratic terms in energy density dominate the dynamics) and the general case. Theevolution profiles of the matter, of the scalar field and of the scale factor of theUniverse are obtained for different values of the parameters of the model and of theequations of state of the normal and dark matter. The equation describing thetime evolution of the ratio of the energy densities of the dark and the normalmatter is also obtained. The ratio depends on the rate of energy flow between thebulk and the brane. The observational constraint of an approximately constantratio of the dark and the baryonic matter requires that the dark matter must benon-relativistic (cold). The model predicts a reheating temperature of the order of3 × 106 GeV, a brane tensionof the order of 1025 GeV4, and the composition of the Universe obtained is consistent with the observationaldata.