Bulk-Brane Matching in Bianchi-Types Brane World

O Sevinc,E Gudekli

doi:10.1155/2011/468549

Abstract

We discuss a comprehensive description of the geometry of the brane-world cosmologies, and present bulk and brane structure and matching between brane and bulk metrics. It is clear that the possibility of the matching condition is not always obvious and therefore it requires a separate analysis. In this study we have shown, under the assumption of consideration of the anisotropic metric except Kasner-AdS like, matching procedure is not achieved for Bianchi-types bulk metrics. Examples of this result are presented by the illustrations of the Bianchi-types II and V bulk metrics.

Highlights

Randall and Sundrum RS made an intriguing alternative suggestion in which we reside in a universe, 3 1-dimensional surface the “brane”, of more than four noncompact dimensions. They examine a brane in a space of higher dimension, which is called bulk and it is a slice of anti de Sitter spacetime AdS 1
In this study we have shown, under the assumption of consideration of the anisotropic metric except Kasner-AdS-like, matching procedure is not achieved for Bianchi-types metrics 23
We write the metric in the same manner as 2.1 with the nonzero structure constant of the Lie algebra of one-forms equal to

Summary

Introduction

Randall and Sundrum RS made an intriguing alternative suggestion in which we reside in a universe, 3 1-dimensional surface the “brane” , of more than four noncompact dimensions. For a summary of dynamical systems in the context of cosmology, including Bianchi-type cosmologies, refer to In the these early studies many assumptions were made about the Weyl term, Ei,j , due to the absence of an exact anisotropic bulk solution. This was addressed in for the FLRW and Bianchi I case and shortly after Campos et al found a family of exact, anisotropic solution to the five-dimensional field equation They were able to be explicitly see the relationship between the bulk Weyl curvature and the anisotropy on the brane. Harko and Mak investigated Bianchi-type brane-world behaviour near the singularity and at late times and found that they tend to isotropize for certain matter content They found general solution of the field equations for Bianchi-type I and V in the brane. That the relationship amongst these exponents is more complex than in the Kasner case

Bianchi-Type V

Brane in Anisotropic Bulk

Discussion