Simple fixed-brane gauges in $S_1/Z_2$ braneworlds

TL;DR

This paper investigates the validity of a specific gauge choice in five-dimensional $S_1/Z_2$ braneworld models, demonstrating its construction and applicability to cosmological perturbations through perturbative methods.

Contribution

It shows that a gauge with fixed boundary branes and simplified metric conditions can be constructed perturbatively in certain braneworld scenarios.

Findings

The gauge can be constructed perturbatively after brane collision.

The gauge accommodates cosmological perturbations.

The approach applies to models with a negative cosmological constant.

Abstract

For five-dimensional braneworlds with an $S_1/\mathbb{Z}_2$ orbifold topology for the extra dimension $x^5$, we discuss the validity of recent claims that a gauge exists where the two boundary branes lie at fixed positions and the metric satisfies $g_{\mu 5}=\partial_5 g_{55}=0$ where $\mu$ labels the transverse dimensions. We focus on models where the bulk is empty apart from a negative cosmological constant, which, in the case of cosmological symmetry, implies the existence of a static frame with Schwarzschild-AdS geometry. Considering the background case with the branes moving apart after a collision, we show that such a gauge can be constructed perturbatively, expanding in either the time after collision or the brane velocity. Finally we examine how cosmological perturbations can be accommodated in such a gauge.