Cardy-Verlinde Formula and Asymptotically de Sitter Spaces

TL;DR

This paper investigates whether the entropy of cosmological horizons in asymptotically de Sitter spaces can be described by the Cardy-Verlinde formula, supporting the dS/CFT correspondence across various solutions.

Contribution

It demonstrates that the Cardy-Verlinde formula accurately describes the entropy of horizons in multiple asymptotically de Sitter solutions, including Schwarzschild-de Sitter and topological de Sitter spaces.

Findings

Cardy-Verlinde formula applies to Schwarzschild-de Sitter horizons

Pure de Sitter space entropy fits the formula

Topological de Sitter solutions also conform to the formula

Abstract

In this paper we discuss the question of whether the entropy of cosmological horizon in some asymptotically de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. For the Schwarzschild-de Sitter solution, although the gravitational mass is always negative (in the sense of the prescription in hep-th/0110108 to calculate the conserved charges of asymptotically de Sitter spaces), we find that indeed the entropy of cosmological horizon can be given by using naively the Cardy-Verlinde formula. The entropy of pure de Sitter spaces can also be expressed by the Cardy-Verlinde formula. For the topological de Sitter solutions, which have a cosmological horizon and a naked singularity, the Cardy-Verlinde formula also works well. Our result is in favour of the dS/CFT correspondence.