Non-Gaussianity in Cosmology: from Inflation to the CMB

A period of cosmological inflation, driven by one or more scalar fields, is still the best candidate to solve various problems in the standard Big Bang model. We want to find as many observational constraints on the inflationary quantities as possible, in order to pin down the correct inflation model, which in its turn will provide information about the underlying high-energy theory. Fortunately the non-Gaussianity of inflationary perturbations, as encoded in the bispectrum (or 3-point correlator), has become an important additional way of distinguishing between models, going beyond the linear Gaussian perturbation quantities of the power spectrum. This accreditation thesis provides a review of my work on both the theoretical and the observational aspects of these non-Gaussianities. In the first part a formalism is described, called the long-wavelength formalism, that provides a way to compute the non-Gaussianities in multiple-field inflation. Applications of this formalism to various classes of models, as well as its extensions, are also treated. In the second part an estimator is described, called the binned bispectrum estimator, that allows the extraction of information about non-Gaussianities from data of the cosmic microwave background radiation (CMB). It was in particular one of the three estimators applied to the data of the Planck satellite to provide the currently best constraints on primordial non-Gaussianity. Various extensions of the estimator and results obtained are also discussed. (author)