We solve a continuing controversy when dealing with density fluctuatio
ns in open Friedmann-Robertson-Walker (FRW) universes, on the physical
relevance of a class of exponential modes. We show explicitly and rig
orously that these modes enter the expansion of quantum fields. In the
maximally symmetric de Sitter case, encountered in inflationary model
s, they are excited for fields with a mass below a critical value m(cr
),,. They are seen to be responsible for the breaking of the de Sitter
symmetry for a massless field. We provide an exact calculation of the
power spectrum for any mass. Our method is free of the divergences th
at appear in earlier treatments. We extend the construction to a gener
ic open FRW universe. [S0556-2821(98)01004-2].