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

Abstract

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 ‘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.