The generalized dark radiation and accelerated expansion in brane cosmology

Abstract

The effective Friedman equation describing the evolution of the brane Universe in the cosmology of the Randall–Sundrum model includes a dark (or mirage or Weyl) radiation term. The brane evolution can be interpreted as the motion of the brane in an AdS–Schwarzschild bulk geometry. The energy density of the dark radiation is proportional to the black hole mass. We generalize this result for an AdS bulk space with an arbitrary matter component. We show that the mirage term retains its form, but the black hole mass is replaced by the covariantly defined integrated mass of the bulk matter. As this mass depends explicitly on the scale factor on the brane, the mirage term does not scale as pure radiation. For low energy densities the brane cosmological evolution is that of a four-dimensional Universe with two matter components: the matter localized on the brane and the mirage matter. There is conservation of energy between the two components. This behaviour indicates a duality between the bulk theory and a four-dimensional theory on the brane. The equation of state of the generalized dark radiation is that of a conformal field theory, with an explicit breaking of the conformal invariance through the pressure of the bulk fluid. Accelerated expansion on the brane is possible only if there is negative pressure on the brane or in the bulk, or if the integrated mass of the bulk fluid is negative.