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 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.