Liouville Cosmology
  Liouville string theory is a natural framework for discussing the non-equilibrium evolution of the Universe. It enables non-critical strings to be treated in mathematically consistent manner, in which target time is identified with a world-sheet renormalization-group scale parameter, preserving target-space general coordinate invariance and the existence of an S-matrix. We review our proposals for a unified treatment of inflation and the current acceleration of the Universe. We link the current acceleration of the Universe with the value of the string coupling. In such a scenario, the dilaton plays an essential background role, driving the acceleration of the Universe during the present era after decoupling as a constant during inflation. 
John Ellis, N.E. Mavromatos, D.V. Nanopoulos