Friedmann-Robertson-Walker brane cosmological equations from the five-dimensional bulk (A)dS black hole

TL;DR

This paper reviews brane cosmological equations in a five-dimensional (A)dS black hole bulk, explores their representation via the Cardy-Verlinde formula, and investigates brane cosmology including Einstein-Gauss-Bonnet gravity and inflation.

Contribution

It introduces a comprehensive analysis of FRW brane equations in various five-dimensional gravities, including their CV representation and implications for brane cosmology with quantum corrections.

Findings

Brane matter can be non-CFT with negative energy density.

Certain Gauss-Bonnet couplings lead to non-positive brane matter energy conditions.

The CV formula can represent brane equations in specific gravity setups.

Abstract

In the first part of this work we review the equations of motion for the brane presented in Friedmann-Robertson-Walker (FRW) form, when bulk is five-dimensional (A)dS Black Hole. The spacelike (timelike) FRW brane equations are considered from the point of view of their representation in the form similar to two-dimensional CFT entropy, so-called Cardy-Verlinde (CV) formula. The following five-dimensional gravities are reviewed: Einstein, Einstein-Maxwell and Einstein with brane quantum corrections. The second part of the work is devoted to study FRW brane equations and their representation in CV form, brane induced matter and brane cosmology in Einstein-Gauss-Bonnet (GB) gravity. In particular, we focus on the inflationary brane cosmology. The energy conditions for brane matter are also analyzed. We show that for some values of GB coupling constant (bulk is AdS BH) the brane matter is not CFT. Its energy density and pressure are not always positive.