CFT and Entropy on the Brane

TL;DR

This paper explores the relationship between a brane-universe in AdS-Schwarzschild space, its induced radiation-dominated FRW geometry, and the entropy of a dual strongly coupled CFT, providing new insights into cosmological entropy bounds.

Contribution

It establishes exact formulas linking brane cosmology, black hole horizon crossing, and CFT entropy, connecting holographic principles with cosmological dynamics.

Findings

Entropy and temperature relate to the Hubble parameter at the horizon crossing.

Formulas for CFT entropy are valid generally and match FRW equations at the horizon.

Results offer new perspectives on entropy bounds in cosmology.

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.