Bose-Einstein condensation on closed Robertson-Walker spacetimes

In this letter we summarize our analysis of Bose-Einstein condensation on c losed Robertson-Walker spacetimes. In a previous work we defined an adiabat ic KMS state on the Weyl-algebra of the free massive Klein-Gordon field [M. Trucks, M. Keyl, Phys. Lett. B 399 (1997) 223, M. Trucks, Commun. Math. Ph ys. 197 (1998) 387]. This state describes a free Bose gas on Robertson-Walk er spacetimes. We use this state to analyze the possibility of Bose-Einstei n 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 . (C) 1998 Elsevier Science B.V. All rights reserved.