Some spaces are more equal than others

The standard Concordance Model of cosmology is supported by many different types of cosmological observations. However, it allows many different possibilities for three-dimensional comoving space, of different curvatures and different topologies. We have a theory linking curvature to matter-energy density (general relativity), but we don't yet have a theory relating topology to other physical properties of the Universe. A demonstration of how gravity, geometry, topology and inhomogeneity together give one way of comparing different spaces will be presented, firstly in a simple example, and then in some more general cases. This theoretical result will be compared to observational analyses of WMAP data.