Braneworld Cosmology in (Anti)--de Sitter Einstein--Gauss--Bonnet--Maxwell Gravity

TL;DR

This paper explores braneworld cosmology within a five-dimensional Einstein-Gauss-Bonnet-Maxwell framework, deriving effective Friedmann equations and analyzing the asymptotic behavior of the brane universe, highlighting the role of boundary terms and bulk action finiteness.

Contribution

It introduces a derivation of the effective Friedmann equation for a brane in a charged (Anti)-de Sitter black hole background within Einstein-Gauss-Bonnet-Maxwell gravity, including necessary boundary terms.

Findings

Solutions with zero spatial volume are unphysical.

Bulk action finiteness implies vanishing effective cosmological constant.

An analogy between Friedmann and Cardy-Verlinde formulas is established.

Abstract

Braneworld cosmology for a domain wall embedded in the charged (Anti)-de Sitter-Schwarzschildblack hole of the five--dimensional Einstein-Gauss-Bonnet-Maxwell theory is considered. The effective Friedmann equation for the brane is derived by introducing the necessary surface counterterms required for a well-defined variational principlein the Gauss--Bonnet theory and for the finiteness of the bulk space. The asymptotic dynamics of the brane cosmology is determined and it is found that solutions with vanishingly small spatial volume are unphysical. The finiteness of the bulk action is related to the vanishing of the effective cosmological constant on the brane. An analogy between the Friedmann equation and a generalized Cardy--Verlinde formula is drawn.