On Quantum Statistical Mechanics on Robertson-Walker Spacetimes
We review our approach to quantum statistical mechanics on Robertson-Walker space-times using the framework of algebraic quantum eld theory on curved spacetimes. Our approach starts with the deenition of an adiabatic KMS state. This state approximates a thermal equilibrium state of a free Bose gas on Robertson-Walker spacetimes. Furthermore it is of Hadamard form, i.e. a physically relevant state in the philosophy of algebraic quantum eld theory. We start an analysis of the possibility of Bose-Einstein condensation on closed Robertson-Walker spacetimes, taking into account the eeects of niteness of the spatial volume of a closed Robertson-Walker spacetime. It turns out that a critical radius can be deened. Below this radius, the gas is in a condensed state, while the condensate disappears above the radius.