  We propose a canonical description of the dynamics of quantum systems on a
class of Robertson-Walker space-times. We show that the worldline of an
observer in such space-times determines a unique orbit in the local conformal
group SO(4,1) of the space-time and that this orbit determines a unique
transport on the space-time. For a quantum system on the space-time modeled by
a net of local algebras, the associated dynamics is expressed via a suitable
family of ``propagators''. In the best of situations, this dynamics is
covariant, but more typically the dynamics will be ``quasi-covariant'' in a
sense we make precise. We then show by using our technique of ``transplanting''
states and nets of local algebras from de Sitter space to Robertson-Walker
space that there exist quantum systems on Robertson-Walker spaces with
quasi-covariant dynamics. The transplanted state is locally passive, in an
appropriate sense, with respect to this dynamics.
