Cosmic vorticity on the brane

TL;DR

This paper investigates vector perturbations in brane-world cosmologies, revealing that during inflation, bulk vector modes obey wave equations similar to tensor modes but lack normalisable zero-modes without matter sources.

Contribution

It demonstrates that bulk vector perturbations follow a wave equation akin to tensor modes during inflation but do not possess normalisable zero-modes in vacuum conditions.

Findings

Bulk vector perturbations obey a wave equation similar to tensor modes during inflation.

No normalisable zero-mode exists without matter sources in the vacuum bulk.

The spectrum consists of a continuum of massive modes that remain in the vacuum state.

Abstract

We study vector perturbations about four-dimensional brane-world cosmologies embedded in a five-dimensional vacuum bulk. Even in the absence of matter perturbations, vector perturbations in the bulk metric can support vector metric perturbations on the brane. We show that during de Sitter inflation on the brane vector perturbations in the bulk obey the same wave equation for a massless five-dimensional field as found for tensor perturbations. However, we present the second-order effective action for vector perturbations and find no normalisable zero-mode in the absence of matter sources. The spectrum of normalisable states is a continuum of massive modes that remain in the vacuum state during inflation.