Standard cosmology from the brane cosmology with a localized matter

Abstract

We discuss the brane cosmology in the 5D anti de Sitter Reissner-Nordstrom (AdSRN$_5$) spacetime. A brane with the tension $σ$ is defined as the edge of an AdSRN$_5$ space with mass $M$ and charge $Q$. In this case we get the CFT-radiation term $(ρ_{CFT})$ from $M$ and the charged dust $(-ρ^2_{cd})$ from $Q^2$ in the Friedmann-like equation. However, this equation is not justified because it contains $ρ_{cd}^2$-term with the negative sign. This is unconventional in view of the standard cosmology. In order to resolve this problem, we introduce a localized dust matter which satisfies $P_{dm}=0$. If $ρ_{dm}=\fr{\sqrt 3}{2}ρ_{cd}$, the unwanted $-ρ_{cd}^2$ is cancelled against $ρ_{dm}^2$ and thus one recovers a standard Friedmann-Robertson-Walker universe with CFT-radiation and dust matter. For the stiff matter consideration, we can set $ρ_{csti}\sim Q^2$ with the negative sign. Here we introduce a massless scalar which plays the role of a stiff matter with $P_{sca}=ρ_{sca}$ to cancel $-ρ_{csti}$. In this case, however, we find a mixed version of the standard and brane cosmologies.