A&A 423, 821-831 (2004)

DOI: 10.1051/0004-6361:20040337

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

**B. F. Roukema**

^{1}, B. Lew^{1}, M. Cechowska^{1}, A. Marecki^{1}and S. Bajtlik^{2}^{1}Torun Centre for Astronomy, N. Copernicus University, ul. Gagarina 11, 87-100 Torun, Poland

e-mail: boud@astro.uni.torun.pl

^{2}Nicolas Copernicus Astronomy Centre, ul. Bartycka 18, 00-716 Warsaw, Poland

(Received 25 February 2004 / Accepted 26 May 2004)

** 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
, 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
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 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
, 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
and their opposites. The six pairs of circles *independently* each
favour a circle angular radius of
11
.
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
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.

**Key words:**cosmology: observations

**--**cosmology: cosmic microwave background

**--**reference systems

SIMBAD Objects

**©**

*ESO 2004*