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The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
This thesis is centered on three main subjects within the theory of inflation and cosmological perturbations: loop corrections to the power spectrum of curvature fluctuations generated during inflation; evolution of cosmological…
I present a streamlined review of how the separate universe approach to cosmological perturbation theory can be used to study the dynamics of long-wavelength scalar perturbations in loop quantum cosmology, and then use it to calculate how…
A short introduction to structure formation is given, followed by a discussion of the possible characteristics of the initial perturbations assuming a generic inflationary origin. Observational data related to large-scale structure and the…
We introduce the "wedge diagram," an intuitive way to illustrate how cosmological models with a classical (non-singular) bounce generically resolve fundamental problems in cosmology. These include the well-known horizon, flatness, and…
The purpose of these lectures is to give a pedagogical introduction to inflation and the production of primordial perturbations, as well as a review of some of the latest developments in this domain. After a short introduction, we review…
We present a full investigation of scalar perturbations in a rather generic model for a regular bouncing universe, where the bounce is triggered by an effective perfect fluid with negative energy density. Long before and after the bounce…
We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive…
In forthcoming years, connections between cosmology and particle physics will be made increasingly important with the advent of a new generation of cosmic microwave background (CMB) experiments. Here, we review a number of these links. Our…
The quantum cosmology of the flat Friedmann-Lema{\^i}tre-Robertson-Walker Universe, filled with a scalar field, is considered in the de Broglie-Bohm (dBB) interpretation framework. A stiff-matter quantum bounce solution is obtained. The…
Bouncing cosmologies, suggested by String/M-theory, may provide an alternative to standard inflation to account for the origin of inhomogeneities in our universe. The fundamental question regards the correct way to evolve the scalar…
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through…
The theory of cosmological fluctuations assumes that the pre-inflationary state of the universe was the quantum vacuum of a scalar field(s) coupled to gravity. The observed cosmic microwave background fluctuations are then interpreted as…
These lectures are intended to give a pedagogical introduction to the main current picture of the very early universe. After elementary reviews of general relativity and of the standard Big Bang model, the following subjects are discussed:…
By quantising the background as well as the perturbations in a simple one fluid model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical predictions. In a…
In this thesis we investigate several aspects related to the theory of fluctuations in the Cosmic Microwave Background. We develop a new algorithm to calculate the angular power spectrum of the anisotropies which is two orders of magnitude…
Bouncing cosmologies, while offering a compelling alternative to inflationary models, face challenges from the growth of vector perturbations during the contracting phase. While linear vector instabilities can be avoided with specific…
We apply several methods related to the WKB approximation to study cosmological perturbations during inflation, obtaining the full power spectra of scalar and tensor perturbations to first and to second order in the slow-roll parameters. We…
This chapter provides a review of the frameworks developed for cosmological perturbation theory in loop quantum cosmology, and applications to various models of the early universe including inflation, ekpyrosis and the matter bounce, with…
We construct a class of viable bouncing models that are conformally related to cosmological inflation. There are three main difficulties in constructing such a model: (i) A stable (attractor) solution, (ii) A non-singular bounce, and (iii)…