Single-Brane Cosmological Solutions with a Stable Compact Extra Dimension

Abstract

We consider 5-dimensional cosmological solutions of a single brane. The correct cosmology on the brane, i.e., governed by the standard 4-dimensional Friedmann equation, and stable compactification of the extra dimension is guaranteed by the existence of a non-vanishing \hat{T}^5_5 which is proportional to the 4-dimensional trace of the energy-momentum tensor. We show that this component of the energy-momentum tensor arises from the backreaction of the dilaton coupling to the brane. The same positive features are exhibited in solutions found in the presence of non-vanishing cosmological constants both on the brane (Λ_{br}) and in the bulk (Λ_B). Moreover, the restoration of the Friedmann equation, with the correct sign, takes place for both signs of $Λ_B$ so long as the sign of $Λ_{br}$ is opposite $Λ_B$ in order to cancel the energy densities of the two cosmological constants. We further extend our single-brane thin-wall solution to allow a brane with finite thickness.