Bianchi type I space and the stability of inflationary Friedmann-Robertson-Walker space

TL;DR

This paper analyzes the stability of Bianchi type I universes within pure gravity, showing that isotropic instabilities extend to anisotropic perturbations, impacting the understanding of inflationary cosmological models.

Contribution

It derives a non-redundant field equation for Bianchi type I space and demonstrates the stability properties of inflationary solutions under anisotropic perturbations.

Findings

Unstable isotropic modes remain unstable under anisotropic perturbations.

Derived a simplified, non-redundant field equation for Bianchi type I universe.

Discussed implications for physical theories of the early universe.

Abstract

Stability analysis of the Bianchi type I universe in pure gravity theory is studied in details. We first derive the non-redundant field equation of the system by introducing the generalized Bianchi type I metric. This non-redundant equation reduces to the Friedmann equation in the isotropic limit. It is shown further that any unstable mode of the isotropic perturbation with respect to a de Sitter background is also unstable with respect to anisotropic perturbations. Implications to the choice of physical theories are discussed in details in this paper.