  In this letter we summarize our analysis of Bose-Einstein condensation on
closed Robertson-Walker spacetimes. In a previous work we defined an adiabatic
KMS state on the Weyl-algebra of the free massive Klein-Gordon field. This
state describes a free Bose gas on Robertson-Walker spacetimes. We use this
state to analyze the possibility of Bose-Einstein condensation on closed
Robertson-Walker spacetimes. We take into account the effects due to the
finiteness of the spatial volume and show that they are not relevant in the
early universe. Furthermore we show that a critical radius can be defined. The
condensate disappears above the critical radius.
