  In this work we define a new state on the Weyl algebra of the free massive
scalar Klein-Gordon field on a Robertson-Walker spacetime and prove 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 statistical mechanics on
Robertson-Walker spacetimes in the algebraic framework and the analysis of the
free Bose gas on Robertson-Walker spacetimes. The state reduces to an adiabatic
vacuum state if the temperature is zero and it reduces to the usual KMS state
if the scaling factor in the metric of the Robertson-Walker spacetime is
constant.
  In the second part of our work we discuss the time evolution of adiabatic KMS
states. The time evolution is described in terms of semigroups. We prove the
existence of a propagator on the classical phase space. This defines a time
evolution on the one-particle Hilbert space. We use this time evolution to
analyze the evolution of the two-point function of the KMS state. The inverse
temperature change is proportional to the scale factor in the metric of the
Robertson-Walker spacetime, as one expects for a relativistic Bose gas.
