A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map

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Abstract
Luminet et al. (2003) suggested that WMAP data are better matched by a Poincar\'e dodecahedral FLRW model of global geometry, rather than by an infinite flat model. The analysis by Cornish et al. (2003) for angular radii 25-90 degrees failed to support this. Here, a matched circles analysis specifically designed to detect dodecahedral patterns of matched circles is performed over angular radii in the range 1-40 degrees on the one-year WMAP ILC map, using a correlation statistic and an rms difference statistic. Extreme value distributions of these statistics are calculated for left-handed and right-handed 36 degree `screw motions' (Clifford translations) when matching circles and for a zero (unphysical) rotation. The most correlated circles appear for circle radii of 11\pm1 degrees, for the left-handed screw motion, but not for the right-handed one, nor for the zero rotation. The favoured six dodecahedral face centres in galactic coordinates are (l,b)= (252, +65), (51, +51), (144,+38), (207,+10), (271,+3), (332,+25) and their opposites. The six pairs of circles_independently_ each favour a circle angular radius of 11\pm1 degrees. Whether or not these six circle pairs centred on dodecahedral faces match via a 36 degree rotation only due to unexpected statistical properties of the WMAP ILC map, or whether they match due to global geometry, it is clear that the WMAP ILC map has some unusual statistical properties which mimic a potentially interesting cosmological signal. The software for reading the WMAP data and for carrying out this analysis are released under the GNU General Public License.

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