Holographic principle in the Binetruy-Deffayet-Langlois brane cosmology

We study the holographic principle in the brane cosmology. Especially we describe how to accommodate the five-dimensional anti--de Sitter Schwarzschild (AdSS₅) black hole in the Binetruy-Deffayet-Langlois (BDL) approach of brane cosmology. It is easy to make a connection between a mass M of the AdSS₅ black hole and a conformal field theory (CFT) radiation dominated universe on the brane in the moving domain wall approach. But this is not established in the BDL approach. In this case we use two parameters C₁ and C₂ in the Friedmann equation. These arise from integration and are really related to the choice of initial bulk matter. If one chooses a bulk energy density ρB to account for a mass M of the AdSS₅ black hole and the static fifth dimension, a CFT-radiation term with ρCFT~M/a⁴ comes out from the bulk matter without introducing a localized matter distribution on the brane. This means that the holographic principle can be established in the BDL brane cosmology.