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

TL;DR

This work examines FRW brane cosmology with a 5D (A)dS bulk black hole and demonstrates that brane dynamics can be recast in Cardy-Verlinde entropy form across several gravitational theories. By analyzing AdS/dS Schwarzschild backgrounds and including Maxwell fields and quantum corrections, it reveals conditions under which the induced brane matter is radiation-like (CFT) or non-CFT, and shows how energy conditions may be violated for certain Gauss-Bonnet couplings. The CV perspective links brane cosmology to bulk thermodynamics, clarifying holographic entropy bounds and inflationary de Sitter brane solutions (Brane New World). The results have implications for holography in higher-derivative gravity and the role of quantum effects in brane-world cosmology.

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.