Instability of 1-loop superstring cosmology
  A stability analysis is made in the context of the previously discovered non-singular cosmological solution from 1-loop corrected superstring effective action. We found that this solution has an instability in graviton mode, which is shown to have a close relation to the avoidance of initial singularity via energy condition. We also estimate the condition for the breakdown of the background solution due to the overdominance of the graviton. 
Shinsuke Kawai, Masa-aki Sakagami and Jiro Soda