Thermal history of the string universe
  Thermal history of the string universe based on the Brandenberger and Vafa's scenario is examined. The analysis thereby provides a theoretical foundation of the string universe scenario. Especially the picture of the initial oscillating phase is shown to be natural from the thermodynamical point of view. A new tool is employed to evaluate the multi state density of the string gas. This analysis points out that the well-known functional form of the multi state density is not applicable for the important region $T \leq T_H$, and derives a correct form of it. 
H. Cateau & K. Sumiyoshi