Bianchi type-II cosmological model: some remarks

TL;DR

This paper examines the Bianchi type-II cosmological model, revealing that off-diagonal Einstein tensor components impose strict restrictions on matter distribution, especially requiring isotropy in locally rotationally symmetric cases.

Contribution

It demonstrates that non-zero off-diagonal Einstein tensor components restrict matter distribution, proving isotropy in LRS Bianchi type-II models with diagonal energy-momentum tensors.

Findings

Off-diagonal Einstein tensor components impose restrictions on matter distribution.

In LRS Bianchi type-II models, matter must be isotropic if energy-momentum tensor is diagonal.

The study clarifies the relationship between geometric restrictions and matter properties in Bianchi cosmologies.

Abstract

Within the framework of Bianchi type-II (BII) cosmological model the behavior of matter distribution has been considered. It is shown that the non-zero off-diagonal component of Einstein tensor implies some severe restriction on the choice of matter distribution. In particular for a locally rotationally symmetric Bianchi type-II (LRS BII) space-time it is proved that the matter distribution should be strictly isotropic if the corresponding matter field possesses only non-zero diagonal components of the energy-momentum tensor.