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.

It has been suggested by Roukema and coworkers (hereafter R04) that the topology of the Universe as probed by the "matched circles" method using the first year release of the WMAP CMB data, might be that of the Poincaré dodecahedral space (PDS) model. An excess in the correlation of the "identified circles" was reported by R04, for circles of angular radius of ∼11• for a relative phase twist −36• , hinting that this could be due to a Clifford translation, if the hypothesized model were true. R04 did not however specify the statistical significance of the correlation signal. We investigate the statistical significance of the signal using Monte Carlo CMB simulations in a simply connected Universe, and present an updated analysis using the three-year WMAP data. We find that our analyses of the first and three year WMAP data provide results that are consistent with the simply connected space at a confidence level as low as 68%.

We re-examine the evidence of hemispherical power asymmetry, detected in the cosmic microwave background (CMB) WMAP (Wilkinson Microwave Anisotropy Probe) data using a new method. We use a data filtering, preprocessing , and a statistical approach different from those used previously, and pursue an independent method of parameter estimation. First, we analyze the hemispherical variance ratios and compare these with simulated distributions. Secondly, working within a previously proposed CMB bipolar modulation model, we constrain the model parameters: the amplitude and the orientation of the modulation field as a function of various multipole bins. Finally, we select three ranges of multipoles leading to the most anomalous signals, and we process corresponding 100 Gaussian, random field (GRF) simulations, treated as observational data, to further test the statistical significance and robustness of the hemispherical power asymmetry. For our analysis we use the Internally-Linearly-Coadded (ILC) full sky map, and the KQ75 cut sky V channel foregrounds reduced map of the WMAP five year data (V5). We constrain the modulation parameters using a generic maximum a posteriori method.In particular, we find differences in hemispherical power distribution, which when described in terms of a model with bipolar modulation field, exclude the field amplitude value of the isotropic model A = 0 at confidence level of ∼ 99.5% ( ∼ 99.4%) in the multipole range ℓ ∈ [7, 19] (ℓ ∈ [7, 79]) in the V5 data, and at the confidence level ∼ 99.9% in the multipole range ℓ ∈ [7, 39] in the ILC5 data, with the best fit (modal PDF) values in these particular multipole ranges of A = 0.21 (A = 0.21) and A = 0.15 respectively.However, we also point out that similar or larger significances (in terms of rejecting the isotropic model), and large best-fit modulation amplitudes are obtained in GRF simulations as well, which reduces the overall significance of the CMB power asymmetry down to only about 94% (95%) in the V5 data, in the range ℓ ∈ [7, 19] (ℓ ∈ [7, 79]).

We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) foreground reduced temperature maps. We also test cross-channel difference maps to constrain levels of residual foreground contamination and systematic uncertainties. We divide the sky into regions of varying size and shape and measure the first four moments of the one-point distribution within these regions, and using their simulated spatial distributions we test the statistical isotropy and Gaussianity hypotheses. By randomly varying orientations of these regions, we sample the underlying CMB field in a new manner, that offers a richer exploration of the data content, and avoids possible biasing due to a single choice of sky division. In our analysis we account for all two-point correlations between different regions and also show the impact on the results when these correlations are neglected. The statistical significance is assessed via comparison with realistic Monte Carlo simulations. We find the three-year WMAP maps to agree well with the isotropic, Gaussian random field simulations as probed by regions corresponding to the angular scales ranging from 6° to 30° at 68% confidence level (CL). We report a strong, anomalous (99.8% CL) dipole ‘excess’ in the V band of the three-year WMAP data and also in the V band of the WMAP five-year data (99.3% CL). Using our statistics, we notice large scale hemispherical power asymmetry, and find that it is not highly statistically significant in the WMAP three-year data () at scales . The significance is even smaller if multipoles up to are considered (∼90% CL). We give constraints on the amplitude of the previously proposed CMB dipole modulation field parameter. We find some hints of foreground contamination in the form of a locally strong, anomalous kurtosis excess in the Q+V +W co-added map, which however is not significant globally. We easily detect the residual foregrounds in cross-band difference maps at rms level (at scales ) and limit the systematical uncertainties to (at scales ).