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

A stability analysis of the Bianchi type-I universe in pure gravity theory is studied in detail. We first derive the nonredundant field equation of the system by introducing the generalized Bianchi type-I metric. This nonredundant 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. The implications of the choice of physical theories are discussed in detail in this paper.