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.
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.
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