Concepts of non-linear data analysis applied to the search of non-Gaussianities in the CMB

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.