Universal Approach to Cosmological Singularities in Two Dimensional   Dilaton Gravity
  We show that in a large class of two dimensional models with conformal matter fields, the semiclassical cosmological solutions have a weak coupling singularity if the classical matter content is below a certain threshold. This threshold and the approach to the singularity are model-independent. When the matter fields are not conformally invariant, the singularity persists if the quantum state is the vacuum near the singularity, and could dissappear for other quantum states. 
G.N. Martin and F.D. Mazzitelli