Rotational Perturbations of Friedmann-Robertson-Walker Type Brane-World Cosmological Models

TL;DR

This paper investigates rotational perturbations in brane-world cosmological models, deriving equations that restrict angular velocity behavior and identifying models where such perturbations decay over time, similar to general relativity.

Contribution

It derives the rotation equation for brane-world models under slow rotation and explores integrable cases, revealing decay of rotational perturbations and a specific inflationary model.

Findings

Rotational perturbations decay with the universe's expansion.

Derived a rotation equation linking metric perturbations to matter angular velocity.

Identified a unique inflationary brane-world cosmological model.

Abstract

First order rotational perturbations of the Friedmann-Robertson-Walker metric are considered in the framework of the brane-world cosmological models. A rotation equation, relating the perturbations of the metric tensor to the angular velocity of the matter on the brane is derived under the assumption of slow rotation. The mathematical structure of the rotation equation imposes strong restrictions on the temporal and spatial dependence of the brane matter angular velocity. The study of the integrable cases of the rotation equation leads to three distinct models, which are considered in detail. As a general result we find that, similarly to the general relativistic case, the rotational perturbations decay due to the expansion of the matter on the brane. One of the obtained consistency conditions leads to a particular, purely inflationary brane-world cosmological model, with the cosmological fluid obeying a non-linear barotropic equation of state.