Averaging in cosmological models using scalars
  The averaging problem in cosmology is of considerable importance for the
correct interpretation of cosmological data. A rigorous mathematical definition
of averaging in a cosmological model is necessary. In general, a spacetime is
completely characterized by its scalar curvature invariants, and this suggests
a particular spacetime averaging scheme based entirely on scalars. We clearly
identify the problems of averaging in a cosmological model. We then present a
precise definition of a cosmological model, and based upon this definition, we
propose an averaging scheme in terms of scalar curvature invariants. This
scheme is illustrated in a simple static spherically symmetric perfect fluid
cosmological spacetime, where the averaging scales are clearly identified.
