Cosmological Predictions from the Primordial Universe: Non-Gaussianities

Non-Gaussian statistics in the distribution of large scale structure, and in temperature fluctuations of the cosmic microwave background, can be used to constrain inflationary models. Data on the cosmic microwave background from Planck (2015) is able to provide up-to-date bounds on parameters controlling the degree of non-Gaussianity in given models of inflation, thus favouring or disfavouring certain models. Starting from the statistics of random fields, this essay reviews non-Gaussianity from first principles, including Juan Maldacena's seminal calculation of non-Gaussianity in single-field, slow-roll inflation. Following this, models whereby the initial quantum state of inflation is so-called non-Bunch-Davis is considered. The non-Gaussian signature produced by such models is quantified, and parameters controlling the degree of non-Gaussianity are constrained using data from Planck (2015).