Cardy-Verlinde Formula and Holographic Dark Energy

TL;DR

This paper explores the connection between the Cardy-Verlinde formula, holographic dark energy, and cosmological constants, showing how entropy and energy separation relate to dark energy in various dimensions.

Contribution

It demonstrates that the Cardy-Verlinde formula can derive holographic dark energy and links it to the Friedmann equation using different entropy bounds.

Findings

The intrinsic energy matches recent dark energy proposals.

The cosmological constant derived aligns with holographic dark energy models.

The formula applies in arbitrary dimensions.

Abstract

If we separate energy in a holographic theory into an extensive part and an intrinsic part, where the extensive part is given by the cosmological constant, and assume entropy be given by the Gibbon-Hawking formula, the Cardy-Verlinde formula then implies an intrinsic part which agrees with a term recently proposed by Hsu and Zee. Moreover, the cosmological constant so derived is in the form of the holographic dark energy, and the coefficient is just the one proposed recently by Li. If we replace the entropy by the so-called Hubble bound, we show that the Cardy-Verlinde formula is the same as the Friedmann equation in which the intrinsic energy is always dark energy. We work in an arbitrary dimension.