dS/CFT Duality on the Brane with a Topological Twist

TL;DR

This paper explores the holographic properties of a brane universe in a topological de Sitter background, demonstrating that many features of AdS/CFT duality extend to dS/CFT scenarios, including thermodynamics and entropy relations.

Contribution

It shows that the dS/CFT correspondence applies to brane worlds with topological de Sitter bulk, extending holographic principles beyond AdS spaces.

Findings

Friedmann-like equations describe brane evolution.

Holographic entropy relations persist in dS backgrounds.

Coincidences occur when the brane crosses the horizon.

Abstract

We consider a brane universe in an asymptotically de Sitter background spacetime of arbitrary dimensionality. In particular, the bulk spacetime is described by a ``topological de Sitter'' solution, which has recently been investigated by Cai, Myung and Zhang. In the current study, we begin by showing that the brane evolution is described by Friedmann-like equations for radiative matter. Next, on the basis of the dS/CFT correspondence, we identify the thermodynamic properties of the brane universe. We then demonstrate that many (if not all) of the holographic aspects of analogous AdS-bulk scenarios persist. These include a (generalized) Cardy-Verlinde form for the CFT entropy and various coincidences when the brane crosses the cosmological horizon.