Peculiar features in the cosmic microwave background radiation
In this thesis, I develop statistics capable of detecting peculiar features in current observations of the cosmic microwave background (CMB) radiation. Such tools scrutinise the very foundations of standard cosmological models. Evidence of peculiar features in the CMB may require a reassessment of these building blocks. More likely, any features may be artefacts of some non-cosmological signal. Nevertheless, whether the origin of these strange attributes is primordial or local, their discovery would be instructive. Existing statistical tools focus on the amplitude of the spherical harmonic coefficients, I look instead at their phases. The method I form checks for the uniformity of the distribution of phase angles using a non-parametric descriptor, which is known as Kuiper's statistic. The method is applied to the COBE-DMR and WMAP sky maps, and departures from uniformity are found in both. The results probably reflect Galactic contamination or the known variation of signal-to-noise across the sky rather than primordial non-Gaussianity. Next, the statistic is adjusted to probe the topology of the universe. The new method exploits the existence of correlations in the phases of the CMB temperature pattern associated with matched pairs of circles seen in the CMB in universes with non-trivial topologies. After this, I turn our attention to the issue of Galactic foreground signals. A diagnostic of foreground contamination is developed based around the Faraday rotation measures (RM) of extragalactic sources. Statistically significant correlations of RM with the preliminary WMAP individual frequency maps are found. These correlations remain significant in CMB-only maps. Later, I use catalogues of rotation measures to construct a template of the Galactic sky. The RM maps may be used as templates for CMB foreground analysis. This idea is illustrated with a cross-correlation analysis between the WMAP data and our maps. I find a significant cross-correlation, again indicating the presence of significant residual contamination. Problems and future developments are discussed at the end.