Generality of Singularity Avoidance in Superstring Theory: Anisotropic Case

In one-loop string effective action, we study a generality of non-singular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi I and IX type spacetimes. We find that nonsingular solutions still exist in Bianchi I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in Bianchi IX model. Non-existence of nonsingular Bianchi IX universe may be consistent with the analysis by Kawai, Sakagami and Soda, i.e. the tensor mode perturbations against nonsingular flat Friedmann universe are unstable, because Bianchi IX model can be regarded as a closed Friedmann universe with a single gravitational wave. So based on these facts, we may conclude the nonsingular universe is found in isotropic case is generally unstable, a singularity avoidance may not work in the present model.