On the Hagedorn behavior of the superstring propating in a cosmological time dependent background

In this work the LvN quantization of the type IIB superstring is carried on in a time dependent plane wave background with a constant self-dual Ramond-Ramond 5-form and a linear dilaton in the light-like direction. Such an endeavour allows us to define an invariant density matrix and study important issues in real time string thermodynamics. In particular, the Hagendorn temperature is calculated as function of the thermalization time.