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Stability conditions for a class of anisotropically inflating solutions in the Bianchi type II background space are shown explicitly in this paper. These inflating solutions were known to break the cosmic no-hair theorem such that they do not approach the de Sitter universe at large times. It can be shown that unstable modes of the anisotropic perturbations always exist for this class of expanding solutions. As a result, we show that these set of anisotropically expanding solutions are unstable against anisotropic perturbations in the Bianchi type II space.

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We show that a Brans-Dicke model admits some anisotropically inflating solutions which are identical to the solutions found in a higher derivative pure gravity theory. These inflating solutions were shown to break the cosmic no-hair theorem such that they do not approach the de Sitter universe at large times. The stability conditions of these solutions in this scalar-tensor theory are shown explicitly in this paper. It is shown that there exist unstable modes of the anisotropic perturbations. Therefore the inflating solutions are unstable in the scalar-tensor theory.

No abstract