Primordial non-Gaussianity in the cosmological perturbations - CBPF

Part I
Introduction
Our current understanding of the evolution of the universe is based upon the Friedmann-Robertson-
Walker (FRW) cosmological model, or the hot big bang model as it is usually called. The model is
so successful that it has become known as the standard cosmology. times. The FRW cosmology is
so robust that it is possible to make sensible speculations about the universe at times as early as
10 −43 sec after the Big Bang.
The most important feature of our universe is its large scale homogeneity and isotropy. This
feature ensures that observations made from our single point are representative of the universe as a
whole and can therefore be legitimately used to test cosmological models. For most of the twentieth
century, the homogeneity and isotropy of the universe had to be taken as an assumption, known as
the Cosmological Principle. The assumption of isotropy and homogeneity dates back to the earliest
work of Einstein, who made the assumption not based upon observations, but as theorists often do,
to simplify the mathematical analysis. The Cosmological Principle remained an intelligent guess
until firm empirical data, confirming large scale homogeneity and isotropy, were finally obtained
at the end of the twentieth century. The best evidence for the isotropy of the observed universe
Figure 1: The large-scale structure from the 2dF Galaxy Survey
is the uniformity of the temperature of the cosmic microwave background (CMB) radiation: aside
from the observed dipole anisotropy, the temperature difference between two antennas separated by
angles ranging from about 10 arc seconds to 180 ◦ is smaller than about one part in 10 5 . The simplest
interpretation of the dipole anisotropy is that it is the result of our motion relative to the cosmic rest
frame. If the expansion of the universe were not isotropic, the expansion anisotiopy would lead to a
temperature anisotiopy in the CMBR of similar magnitude. Likewise, inhomogeneities in the density
of the universe on the last scattering surface would lead to temperature anisotropies. In this iegard,
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