A class of Bianchi type II expanding solutions in a Lorentz Chern-Simons theory has been known to break the cosmic no-hair theorem. These solutions do not approach the late-time de Sitter Universe. We will show that there are two independent solutions classified by the parameter $p$ for each given cosmological constant $\Lambda$. One of them is in the small-$p$ phase; the other solution is in the large-$p$ phase. It can be shown that an unstable mode always exists for the solution in its small-$p$ phase that comes with smaller energy $T_{00}$ and $T_{00}+T/2$. The result indicates that the large-$p$ phase is unlikely to be stable from an observation of a modified version of Wald’s theorem.

• Received 19 June 2011

DOI:https://doi.org/10.1103/PhysRevD.84.063014