PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

1.1. THE CONCORDANT, BACKGROUND COSMOLOGICAL MODEL
era. In the latter part of the thesis, apart from considering the effects of the primordial
features on the formation of halos, we shall outline a method that utilizes the observations
of the Lyman (Ly)-α forest to arrive at constraints on the primordial non-Gaussianity.
The remainder of this introductory chapter is organized as follows. In the next section,
we shall sketch the concordant, background cosmological model that has been arrived
at from a variety of observations. After highlighting the drawbacks of the hot big bang
model, in Section 1.2, we shall outline as to how the inflationary scenario, even as it helps
in overcoming these difficulties, offers a mechanism for the creation of the perturbations.
We shall also present a few essential details concerning linear perturbation theory, and
discuss how the conventional power law perturbation spectra compare with the observations
of the CMB anisotropies. In Section 1.3, we shall briefly discuss the generation
of non-Gaussianities during inflation, which is one of the key issues studied in this thesis.
We shall outline preheating, viz. the epoch that immediately follows inflation, in
Section 1.4, while Section 1.5 contains some relevant details pertaining to the formation
of structure during late times. In Section 1.6, we shall provide a chapter wise outline
of the thesis. We shall conclude this chapter with a few remarks concerning the various
conventions and notations that we shall adopt throughout this thesis.
1.1 The concordant, background cosmological model
We had mentioned that the homogeneous and isotropic universe is described by the
Friedmann metric. We had also pointed out that various observations indicate the density
of the universe to be close to the critical value, which corresponds to a spatially flat
universe. It is worth noting here that the most direct constraint on the total density of the
universe arises from the location of the first acoustic peak in the CMB (in this context, see,
for instance, Refs. [6, 18, 19]). A spatially flat, (3 + 1)-dimensional Friedmann universe
that is characterized by the scale factor a(t) is described by the line-element
ds 2 = dt 2 −a 2 (t)dx 2 = a 2 (η) ( dη 2 −dx 2) , (1.1)
where, recall that, t represents the cosmic time, while η = ∫ dt/a denotes the conformal
time coordinate.
The dynamics of the scale factor a(t) is governed by the Einstein equations, which, in
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