CFT and Entropy on the Brane

Abstract

We consider a brane-universe in the background of an Anti-de Sitter/ Schwarschild geometry. We show that the induced geometry of the brane is exactly given by that of a standard radiation dominated FRW-universe. The radiation is represented by a strongly coupled CFT with an AdS-dual description. We show that when the brane crosses the horizon of the AdS-black hole the entropy and temperature are simply expressed in the Hubble constant and its time derivative. We present formulas for the entropy of the CFT which are generally valid, and which at the horizon coincide with the FRW equations. These results shed new light on recently proposed entropy bounds in the context of cosmology.

Figures (2)

• Figure 1: Penrose diagram of an $AdS_{n+2}$-Schwarzschild black hole with the trajectory of the brane. The brane originates in the past singularity, expands to a certain size and subsequently falls into the future singularity as it re-collapses. The dots indicate the moments when the brane crosses the black hole horizon.
• Figure 2: Diagram of Euclidean $AdS_{n+2}$-Schwarzschild with the trajectory of the brane. The horizon is represented by the dot in the middle of the diagram; only the region $a\geq a_H$ is drawn. The brane originates at spatial infinity, collapses to a certain miminal size and subsequently re-expands. It remains outside of the black hole horizon during the entire evolution.