The Cosmic Microwave Background (CMB) is a unique probe of cosmological parameters and conditions, and allows us to constrain not only models of structure formation, but also the large-scale properties of space itself. For instance, there is a connection between anisotropy in the CMB and the topology of the Universe: modifications of the CMB power spectrum are caused by the fact that only certain fluctuation modes are allowed by the boundary conditions, just as the fundamental tone and its overtones give information about the geometry inside a flute.
Projects:(1.) The cosmic quadrupole on its own is anomalous at the 1-in-20 level by being low (the cut-sky quadrupole measured by the WMAP team is more strikingly low, apparently due to a coincidence in the orientation of our Galaxy of no cosmological significance); (2.) The cosmic octopole on its own is anomalous at the 1-in-20 level by being very planar; (3.) The alignment between the quadrupole and octopole is anomalous at the 1-in-60 level.
Although the a priori chance of all three occurring is 1 in 24000, the
multitude of alternative anomalies one could have looked for dilutes the
significance of such a posteriori statistics.
The simplest small universe model where the universe has toroidal topology
with one small dimension of order half the horizon scale, in the direction towards
Virgo, could explain the three items above. However, we rule this model out
using two topological tests: the S-statistic and the matched circle test.