Anisotropy in Bianchi-type brane cosmologies

TL;DR

This paper investigates the initial anisotropy behavior of Bianchi-type brane cosmologies, finding that for non-zero pressure fluids, the initial singular state is isotropic, with specific solutions for different Bianchi types.

Contribution

It derives exact analytical solutions for the anisotropy evolution in Bianchi brane models, revealing isotropy at the initial singularity for fluids with linear equations of state.

Findings

Initial singularity is isotropic for fluids with non-zero pressure.

Exact solutions for Bianchi I and V types are obtained.

Initial anisotropy matches standard cosmology for dust-filled models.

Abstract

The behavior near the initial singular state of the anisotropy parameter of the arbitrary type, homogeneous and anisotropic Bianchi models is considered in the framework of the brane world cosmological models. The matter content on the brane is assumed to be an isotropic perfect cosmological fluid, obeying a barotropic equation of state. To obtain the value of the anisotropy parameter at an arbitrary moment an evolution equation is derived, describing the dynamics of the anisotropy as a function of the volume scale factor of the Universe. The general solution of this equation can be obtained in an exact analytical form for the Bianchi I and V types and in a closed form for all other homogeneous and anisotropic geometries. The study of the values of the anisotropy in the limit of small times shows that for all Bianchi type space-times filled with a non-zero pressure cosmological fluid, obeying a linear barotropic equation of state, the initial singular state on the brane is isotropic. This result is obtained by assuming that in the limit of small times the asymptotic behavior of the scale factors is of Kasner-type. For brane worlds filled with dust, the initial values of the anisotropy coincide in both brane world and standard four-dimensional general relativistic cosmologies.