Generality of singularity avoidance in superstring theory: Anisotropic case

In the one-loop string effective action, we study a generality of nonsingular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi type-I and -IX spacetimes. We find that nonsingular solutions still exist in the Bianchi type-I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in the Bianchi type-IX model. The nonexistence of a nonsingular Bianchi type-IX universe may be consistent with the analysis of Kawai, Sakagami, and Soda; i.e., the tensor-mode perturbations against a nonsingular flat Friedmann universe are unstable, because the Bianchi type-IX model is regarded as a closed Friedmann universe with a single gravitational wave. With the stability analysis of Kawai, Sakagami, and Soda, the nonsingular universe found in the isotropic case is unstable, and a singularity avoidance may not work in generic spacetimes.