Stability analysis of the Lorentz Chern-Simons expanding solutions

Abstract

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 $\ensuremath{\Lambda}$. 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.