Statistical Properties of Cosmological Fluctuations

Abstract

In this pedagogical lecture, I introduce some of the basic terminology and description of fluctuating fields as they occur on cosmology. I define various statistical, cosmological and sample homogeneity and explain what is meant by the fair sample hypothesis and cosmic variance. I illustrate these concepts using the simplest second-order statistics, i.e. the two--point correlation function and its Fourier transform the power-spectrum. I then give a brief overview of the properties of information relating to the properties of the phases of the Fourier modes of cosmological fluctuations which is not contained in these simpler statistics. Specifically, I explain how phase information of a particular form (called quadratic phase coupling) is encoded in the three--point correlation function (or, equivalently, the bispectrum).