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

Abstract

Abstract. 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 Poincaré 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 25−90• , 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 1−40• on the oneyear 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 36• "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 α = 11 ± 1• , 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• ) and their opposites. The six pairs of circles independently each favour a circle angular radius of 11 ± 1• . 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 36• 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.

Constraining topology in harmonic space

“…However, it is difficult to quantify the probability of missing matching circles, and other groups have claimed a tentative detection of circles at scales not probed by Cornish et al (see e.g. [11,12]). In this paper we study a different approach which can in principle yield both an optimal test as well as a rigorous assessment of the fundamental detection power of the CMB for a cosmic topology.…”

CMB multipole measurements in the presence of foregrounds

“…These include effects of Galactic foreground emission [43][44][45][46][47] and local structures [48][49][50][51][52][53][54][55][56] as well as theoretical explanations going beyond the CSM and involving compact cosmic topology [13,[57][58][59][60][61][62][63][64][65][66][67][68][69], modified inflation [70][71][72][73][74][75][76][77][78][79][80][81][82][83], or other new physics [84][85][86][87][88][89][90][91][...…”

Constraints on the global topology and size of the universe from the cosmic microwave background

“…Following these arguments, we will focus our attention entirely on the flat case in this work. Details on the Poincaré dodecahedral space and experimental data analysis are given in (Luminet et al 2003;Roukema 2009;Roukema et al 2004Roukema et al , 2008Caillerie et al 2007; Lew & Roukema 2008;Aurich et al 2005b), and other topologies in (Aurich & Lustig 2010;Niarchou & Jaffe 2007;Aurich et al 2006Aurich et al , 2005aCresswell et al 2006;Aurich et al 2005c;Roukema 2005;Aurich et al 2004;Riazuelo et al 2004;Gomero et al 2002a;Bond et al 2000;Mota et al 2005;Gundermann 2005).…”