A KMS-LIKE STATE OF HADAMARD TYPE ON ROBERTSON-WALKER SPACETIMES AND ITS TIME EVOLUTION

In this work we define a new state on the Weyl algebra of the free mas sive scalar Klein-Gordon field on a Robertson-Walker spacetime and pro ve that it is a Hadamard state. The state is supposed to approximate a thermal equilibrium state on a Robertson-Walker spacetime and we call it an adiabatic KMS state. This opens the possibility to do quantum s tatistical mechanics on Robertson-Walker spacetimes in the algebraic f ramework and the analysis of the free Bose gas on Robertson-Walker spa cetimes. The state reduces to an adiabatic vacuum state if the tempera ture is zero and it reduces to the usual KMS state if the scaling fact or in the metric of the Robertson-Walker spacetime is constant. In the second part of our work we discuss the time evolution of adiabatic KM S states. The time evolution is described by a family of propagators o n the classical phase space. With the help of this family, we prove th e existence of a family of propagators on the one-particle Hilbert spa ce. We use these propagators to analyze the evolution of the two-point function of the KMS state. The inverse temperature change is proporti onal to the scale factor in the metric of the Robertson-Walker spaceti me, as one expects for a relativistic Bose gas.