Effect of bulk Lorentz violation on anisotropic brane cosmologies

TL;DR

This paper explores how Lorentz invariance violation in a five-dimensional brane-world affects the evolution of anisotropic cosmologies, revealing a transition from anisotropic to isotropic inflationary phases.

Contribution

It extends Lorentz violation models to five dimensions and provides exact solutions for anisotropic brane cosmologies with detailed analysis of their evolution.

Findings

Early universe anisotropy depends on Lorentz violating parameters and matter equation of state.

Late universe evolution becomes independent of Lorentz violation parameters.

The universe transitions to an isotropic de Sitter inflationary phase.

Abstract

The effect of Lorentz invariance violation in cosmology has attracted a considerable amount of attention. By using a dynamical vector field assumed to point in the bulk direction, with Lorentz invariance holding on the brane, we extend the notation of Lorentz violation in four dimensions to a five-dimensional brane-world. We obtain the general solution of the field equations in an exact parametric form for Bianchi type I space-time, with perfect fluid as a matter source. We show that the brane universe evolves from an isotropic/anisotropic state to an isotropic de Sitter inflationary phase at late time. The early time behavior of anisotropic brane universe is largely dependent on the Lorentz violating parameters $\beta_i, i = 1, 2, 3$ and the equation of state of the matter, while its late time behavior is independent of these parameters.