Stability analysis of Single-Brane with Gauss-Bonnet Term in a Bulk

Abstract

We study single-brane 4 + n dimensions which is embedded in bulk 5 + n dimensions with scalar field and Gauss Bonnet terms in bulk. The brane field equation is obtained by performing a bulk field projection by using the Gauss-Codazzi equation. The Einstein brane field equation is formed into the standard Einstein field equation in the Theory of general relativity with additional terms Gauss Bonnet and extra terms. Furthermore cosmological application obtained by reviewing brane’s spacetime is homogeneous and isotropic. FRW metric is taken with two scale factors that are internal dimensions and external dimensions which have a relationship $b(t)=a(t)^\\gamma$. A dynamic analysis is performed to determine the stability of this model by taking the case of the absence of extra terms. Finally, we get a stable solution for this model occurs when the extra dimension n=2.