Topological properties of the cosmic microwave background polarization map

Rapid progress has been made in observations of the temperature anisotropies of the cosmic microwave background (CMB). These observations have enabled cosmologists to characterize the state of the universe at recombination, and observational efforts are now being directed towards obtaining the polarization map of the CMB. Here we draw an analogy between the CMB polarization map and nematic liquid crystals, pointing out that the two have similar defects. Making use of known results in the theory of defect formation we predict the statistical distribution of defects in the CMB polarization map and provide a novel tool for probing the CMB at large angular scales.