  We enumerate the 4(1+F)+2S independent arbitrary functions of space require
to describe a general relativistic cosmology containing an arbitrary number of
non-interacting fluid (F) and scalar fields (S). Results are also given for
arbitrary space dimension and for higher-order gravity theories, where the
number increases to 16+4F+2S. Both counts are subject to assumptions about
whether the dark energy is a cosmological constant. A more detailed analysis is
provided when global homogeneity is assumed and the functions become constants.
This situation is also studied in the case where the flat and open universes
have compact spatial topologies. This changes the relative generalities
significantly and places new constraints on the types of expansion anisotropy
that are permitted. The most general compact homogeneous universes containing
Friedmann models are spatially flat and described by 8+4F+2S constants.
Comparisons are made with the simple 6-parameter lambda-CDM model and physical
interpretations provided for the parameters needed to describe the most general
cosmological models.
