Covariant and quasi-covariant quantum dynamics in Robertson-Walker spacetimes

We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker spacetimes. We show that the worldline of an observer in such spacetimes determines a unique orbit in the identity component SO0(4,1) of the local conformal group of the spacetime and that this orbit determines a unique transport on the spacetime. For a quantum system on the spacetime modelled 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 'quasicovariant' 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.