A hint of Poincare dodecahedral topology in the WMAP first year sky map

It has recently been suggested by Luminet et al. (2003) that the WMAP data are better matched by a geometry in which the topology is that of a Poincare dodecahedral model and the curvature is "slightly" spherical, rather than by an (effectively) infinite flat model. A general back-to-back matched circles analysis by Cornish et al. (2004) for angular radii in the range 25-90degrees, using a correlation statistic for signal detection, failed to support this. In this paper, a matched circles analysis specifically designed to detect dodecahedral patterns of matched circles is performed over angular radii in the range 1-40degrees on the one-year WMAP data. Signal detection is attempted via a correlation statistic and an rms difference statistic. Extreme value distributions of these statistics are calculated for one orientation of the 36degrees "screw motion" (Clifford translation) when matching circles, for the opposite screw motion, and for a zero (unphysical) rotation. The most correlated circles appear for circle radii of alpha = 11 +/- 1degrees, 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(II), b(II)) approximate to (252degrees, +65degrees), (51degrees, +51degrees), (144degrees, +38degrees), (207degrees, + 10degrees), (271degrees, +3degrees), (332degrees, +25degrees) and their opposites. The six pairs of circles independently each favour a circle angular radius of 11 +/- 1degrees. The temperature fluctuations along the matched circles are plotted and are clearly highly correlated. Whether or not these six circle pairs centred on dodecahedral faces match via a 36degrees 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.