Rotational Perturbations of High Density Matter in the Brane Cosmology

TL;DR

This paper investigates how small rotational perturbations evolve in brane-world cosmological models, showing that their decay or growth depends on the matter's equation of state and the nature of dragging effects, providing insights into early Universe physics.

Contribution

It derives equations for rotational perturbations in brane cosmology considering scalar and tensor dark energy effects, analyzing their evolution for various ultra-high density matter types.

Findings

Rotation decays in perfect dragging scenarios during expansion.

Rotation can increase over time for stiff causal or Chaplygin gas.

Hagedorn fluid leads to smoothing out of rotation during expansion.

Abstract

We consider the evolution of small rotational perturbations, with azimuthal symmetry, of the brane-world cosmological models. The equations describing the temporal, radial, and angular dependence of the perturbations are derived by taking into account the effects of both scalar and tensor parts of the dark energy term on the brane. The time decay of the initial rotation is investigated for several types of equation of state of the ultra-high density cosmological matter. For an expanding Universe, rotation always decays in the case of the perfect dragging, for which the angular velocity of the matter on the brane equals the rotation metric tensor. For non-perfect dragging, the behavior of the rotation is strongly equation of state dependent. For some classes of dense matter, like the stiff causal or the Chaplygin gas, the angular velocity of the matter on the brane is an increasing function of time. For other types of the ultra-dense matter, like the Hagedorn fluid, rotation is smoothed out by the expansion of the Universe. Therefore the study of dynamics of rotational perturbations of brane world models, as well as in general relativity, could provide some insights on the physical properties and equation of state of the cosmological fluid filling the very early Universe.