Cosmological Kaluza-Klein branes in black brane spacetimes

TL;DR

This paper explores the cosmological evolution of a brane in higher-dimensional black brane spacetimes with Kaluza-Klein compactification, revealing early RS-like behavior and deviations at later times due to KK dynamics.

Contribution

It introduces a model of brane cosmology in $D>6$ dimensions with KK compactification, analyzing the transition from RS-like to deviated cosmology as the brane moves outward.

Findings

Early-time cosmology matches RS II model predictions.

Deviations from RS cosmology occur as KK dimensions influence dynamics.

Brane cannot reach spatial infinity regardless of matter content.

Abstract

We discuss the comsological evolution of a brane in the $D(>6)$-dimensional black brane spacetime in the context of the Kaluza-Klein (KK) braneworld scheme, i.e., to consider KK compactification on the brane. The bulk spacetime is composed of two copies of a patch of $D$-dimensional black three-brane solution. The near-horizon geometry is given by $AdS_{5}\times S^{(D-5)}$ while in the asymptotic infinity the spacetime approaches $D$-dimensional Minkowski. We consider the brane motion from the near-horizon region toward the spatial infinity, which induces cosmology on the brane. As is expected, in the early times, namely when the brane is located in the near-horizon region, the effective cosmology on the brane coincides with that in the second Randall-Sundrum (RS II) model. Then, the brane cosmology starts to deviate from the RS type one since the dynamics of KK compactified dimensions becomes significant. We find that the brane Universe cannot reach the asymptotic infinity, irrespectively of the components of matter on the brane.