Cosmological Evolution of a Purely Conical Codimension-2 Brane World

TL;DR

This paper investigates the cosmological evolution of a six-dimensional conical codimension-two brane-world with induced gravity and Gauss-Bonnet terms, revealing fixed points and the effects of anisotropy on the universe's evolution.

Contribution

It introduces a detailed analysis of isotropic and anisotropic matter evolution on a codimension-two brane with specific bulk terms, highlighting the stability and tuning conditions of fixed points.

Findings

Isotropic fixed points are attractors for the system.

The nature of fixed points depends on the bulk cosmological constant Lambda_B.

Anisotropy can be sustained without fine-tuning under certain conditions.

Abstract

We study the cosmological evolution of isotropic matter on an infinitely thin conical codimension-two brane-world. Our analysis is based on the boundary dynamics of a six-dimensional model in the presence of an induced gravity term on the brane and a Gauss-Bonnet term in the bulk. With the assumption that the bulk contains only a cosmological constant Lambda_B, we find that the isotropic evolution of the brane-universe imposes a tuned relation between the energy density and the brane equation of state. The evolution of the system has fixed points (attractors), which correspond to a final state of radiation for Lambda_B=0 and to de Sitter state for Lambda_B>0. Furthermore, considering anisotropic matter on the brane, the tuning of the parameters is lifted, and new regions of the parametric space are available for the cosmological evolution of the brane-universe. The analysis of the dynamics of the system shows that, the isotropic fixed points remain attractors of the system, and for values of Lambda_B which give acceptable cosmological evolution of the equation of state, the line of isotropic tuning is a very weak attractor. The initial conditions, in this case, need to be fine tuned to have an evolution with acceptably small anisotropy.