Holographic entropy on the brane from dS/CFT correspondence

TL;DR

This paper explores the connection between de Sitter space entropy and brane-world conformal field theory, demonstrating an exact match at the black hole horizon using holographic principles.

Contribution

It establishes a precise relationship between dS black hole entropy and brane CFT entropy via the dS/CFT correspondence and FRW equations.

Findings

CFT entropy matches black hole entropy at the horizon

Holographic entropy relationship confirmed for dS Schwarzschild space

Utilizes Cardy-Verlinde formula in a de Sitter context

Abstract

The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT which lives on the brane by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula is discussed. We show that when the time-like brane crosses the black hole horizon of dS Schwarzschild black hole, the entropy of the CFT exactly agrees with the black hole entropy of 5-dimensional dS background.