Nj. Cornish et al., CIRCLES IN THE SKY - FINDING TOPOLOGY WITH THE MICROWAVE BACKGROUND-RADIATION, Classical and quantum gravity, 15(9), 1998, pp. 2657-2670
If the universe is finite and smaller than the distance to the surface
of last scatter, then the signature of the topology of the universe i
s writ large on the microwave background sky. We show that the microwa
ve background will be identified at the intersections of the surface o
f last scattering as seen by different 'copies' of the observer. Since
the surface of last scattering is a 2-sphere, these intersections wil
l be circles, regardless of the background geometry or topology. We th
erefore propose a statistic that is sensitive to all small, locally ho
mogeneous topologies. Here, small means that the distance to the surfa
ce of last scatter is smaller than the 'topology scale' of the univers
e.