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Rossmanith, Gregor (2011): Concepts of non-linear data analysis applied to the search of non-Gaussianities in the CMB. Dissertation, LMU München: Fakultät für Physik



One of the key challenges in Cosmology today is to probe both statistical isotropy and Gaussianity of the primordial density perturbations, which are imprinted in the cosmic microwave background (CMB) radiation. While single-field slow-roll inflation predicts the CMB to fulfil these two characteristics, more complex models may give rise to anisotropy and/or non-Gaussianity. A detection or non-detection allows therefore to discriminate between different models of inflation and significantly improves the understanding of basic conditions of the very early Universe. In this work, a detailed CMB non-Gaussianity and isotropy analysis of the five- and seven-year observations of the WMAP satellite is presented. On the one hand, these investigations are performed by comparing the data set with simulations, which is the usual approach for this kind of analyses. On the other hand, a new model-independent approach is developed and applied in this work. Starting from the random phase hypothesis, so- called surrogate maps are created by shuffling the Fourier phases of the original maps for a chosen scale interval. Any disagreement between the data and these surrogates points towards phase correlations in the original map, and therefore – if systematics and foregrounds can be ruled out – towards a violation of single-field slow roll inflation. The construction of surrogate maps only works for an orthonormal set of Fourier functions on the sphere, which is provided by the spherical harmonics exclusively on a complete sky. For this reason, the surrogate approach is for the first time combined with a transformation of the full sky spherical harmonics to a cut sky version. Both the single surrogate approach as well as the combination with the cut sky transformation are tested thoroughly to assess and then rule out the effects of systematics. Thus, this work not only represents a detailed CMB analysis, but also provides a completely new method to test for scale- dependent higher order correlations in complete or partial spherical data sets, which can be applied in different fields of research. In detail, the applications of the above methods involve the following analyses: First, a detailed study of several frequency bands of the WMAP five-year data release is accomplished by means of a scaling index analysis, whereby the data are compared to simulations. Special attention is paid to anomalous local features, and ways to overcome the problem of boundary effects when excluding foreground-influenced parts of the sky. After this, the surrogate approach is for the first time applied to real CMB data sets. In doing so, several foreground-reduced full sky maps from both the five- and seven-year WMAP observations are used. The analysis includes different scale intervals and a huge amount of checks on possible systematics. Then, another step forward is taken by applying the surrogate approach for the first time to incomplete data sets, again from the WMAP five- and seven-year releases. The Galactic Plane, which is responsible for the largest amount of foreground contribution, is removed by means of several cuts of different sizes. In addition, different techniques for the basis transformation are used. In all of these investigations, remarkable non-Gaussianities and deviations from statistical isotropy are identified. In fact, the surrogate approach shows by far the most significant detection of non-Gaussianity to date. The band-wise analysis shows consistent results for all frequency bands. Despite a thorough search, no candidate for foreground or systematic influences could be found. Therefore, the findings of these analyses have so far to be taken as cosmological, and point on the one hand towards a strong violation of single-field slow-roll inflation, and question on the other hand the concept of statistical isotropy in general. Future analyses of the more precise measurements of the forthcoming PLANCK satellite will yield more information about the origin of the detected anomalies.