The focus of this work is the development of statistical and numerical methods forthe study of non-Gaussian and/or anisotropic features in cosmological surveys of themicrowave sky. We focus on two very different types of non-Gaussian (NG) signals.
The former is primordial non-Gaussianity (PNG), generated in the very Early Universeduring the inflationary expansion stage. In this case the aim of our study will be that ofexploiting the NG component in order to extract useful cosmological information. The latter is non-Gaussianity generated by astrophysical foreground contamination. In thiscase, the goal is instead that of using non-Gaussianity as a tool to help in removingthese spurious, non-cosmological components (of course foregrounds themselves contain
relevant astrophysical information, but the focus in this thesis is on Cosmology, thereforeforegrounds are regarded here only as a contaminant).
Considerable efforts have been put so far in the search for deviations from Gaussianity in the CMB anisotropies, that are expected to provide invaluable information aboutthe Inflationary epoch. Inflation is in fact expected to produce an isotropic and nearly-Gaussian fluctuation field. However, a large amount of models also predicts very small,but highly model dependent NG signatures. This is the main reason behind the largeinterest in primordial NG studies. Of course, the pursuit for primordial non-Gaussianity
must rely on beyond power spectrum statistics. It turns out that the most important higher order correlator produced by interactions during Inflation is the three pointfunction, or, more precisely, its Fourier space counterpart, called the bispectrum. Toovercome the issue of computing the full bispectrum of the observed field, that would require a prohibitive amount of computational time, the search for PNG features is carriedout by fitting theoretically motivated bispectrum templates to the data. Among those,
one can find bispectrum templates with a scale-dependent (SD) bispectrum amplitude.
Such templates have actually received little attention so far in the literature, especiallyas long as NG statistical estimation and data analysis are concerned. This is why a significant part of this thesis will be devoted to the development and application of efficientstatistical pipelines for CMB scale-dependent bispectra estimation. We present here theresults of the estimation of several primordial running bispectra obtained from WMAP9 year and Planck data-set.
iiiThe second part of this thesis deals instead, as mentioned iin the beginning, withthe component separation problem, i.e. the identification of the different sources thatcontributes to the microwave sky brightness. Foreground emission produces several,potentially large, non-Gaussian signatures that can in principle be used to identify andremove the spurious components from the microwave sky maps. Our focus will be onthe development of a foreground cleaning technique relying on the hypothesis that, ifthe data are represented in a proper basis, the foreground signal is sparse. Sparsenessimplies that the majority of the signal is concentrated in few basis elements, that can
be used to fit the corresponding component with a thresholding algorithm. We verifythat the spherical needlet frame has the right properties to disentangle the coherentforeground emission from the isotropic stochastic CMB signal. We will make clear inthe following how sparseness in needlet space is actually in several ways linked to thecoherence, anisotropy and non-Gaussianity of the foreground components.. The mainadvantages of our needlet thresholding technique are that it does not requires multi-frequency information as well as that it can be used in combination with other methods.
Therefore it can represent a valuable tool in experiments with limited frequency coverage,as current ground-based CMB surveys
