Stability of the anisotropically inflating Bianchi type VI expanding solutions

Abstract

A special class of the Bianchi type VI expanding solutions was speculated to break the cosmic no-hair theorem that will not approach the late-time de Sitter solution. We will show that an unstable mode always exists when the perturbation of the field equations is applied to the system. In addition to a model-independent perturbation formula, a simplification is also achieved by the introduction of a $\ensuremath{\delta}R=0$ solution good for quadratic models in all Bianchi spaces. The result shows that this special class of anisotropically expanding solutions is unstable.