Coarse-graining approach to quantum cosmology

We consider a Friedmann-Robertson-Walker model with both classical radiation and a massive (conformally coupled) quantum scalar field in the framework of quantum cosmology. We define a density matrix and introduce a notion of "relevance" which splits this density matrix into a "relevant" and an "irrelevant" part. A "generalized coarse-graining method" is used to obtain the evolution (in Robertson-Walker $a$ "time") of the relevant density matrix, taking into account the back reaction of the irrelevant variables. We discuss the physical basis for the choice of a concept of relevance, and the features of cosmic evolution brought forward by the effective dynamics. In the limit of "small universes," the relevant subdynamics is dissipative.