Holographic principle in the BDL brane cosmology

TL;DR

This paper demonstrates how the holographic principle can be realized within BDL brane cosmology by relating bulk black hole mass to brane universe radiation without localized matter.

Contribution

It shows that the holographic principle can be incorporated into BDL brane cosmology through bulk matter parameters, connecting bulk black hole mass to brane radiation.

Findings

CFT-radiation term derived from bulk matter without localized brane matter

Holographic principle established in BDL brane cosmology

Connection between bulk black hole mass and brane universe radiation

Abstract

We study the holographic principle in the brane cosmology. Especially we describe how to accommodate the 5D anti de Sitter Schwarzschild (AdSS$_5$) 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 AdSS$_5$ 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 $C_1, C_2$ 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 $\rho_B$ to account for a mass $M$ of the AdSS$_5$ black hole and the static fifth dimension, a CFT-radiation term with $\rho_{CFT} \sim M/a^{4}$ 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.