Non-slow-roll and brane inflation: New solutions in a unified picture using the flow formalism
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The inflationary paradigm is one of the basic constituents of the standard cosmological model. By postulating a short period of accelerated expansion of the very early universe, it provides a natural explanation for the origin of structure as well as the flatness and homogeneity of the observable universe. In the simplest models, inflation is driven by a single scalar field ( inflaton ) which evolves slowly along a nearly flat potential. However, no compelling fundamental explanation for inflation has yet been proposed. Another obvious place hence to search for a fundamental theory of inflation is within the landscape of string theory, which predicts a plethora of scalar fields associated with the compactification of extra dimensions, and the configuration of lower-dimensional "branes" moving in a higher-dimensional bulk space. In all cases, the quantum fluctuations of the inflaton can be translated into perturbations in the early universe which are observed as temperature fluctuations in the cosmic microwave background (CMB) radiation. This thesis is a contribution to the effort of investigating the physics of inflation in order to discover new inflationary solutions, and can be divided into four parts. The first three chapters contain an introduction and constitute the first part of this work. We formulate the basic principles of Big Bang, or "standard" cosmology, in the first chapter. Even though the Big Bang theory has proven to be very successful, certain features of the universe can not be explained with the standard picture. We review the paradigm of inflation, initially proposed in 1981, as a mechanism for solving the shortcomings of standard cosmology in chapter 2. In chapter 3 we discuss the implementation of inflation within scalar field theories. The second part of this thesis is presented in chapter 4 where we study the evolution of a canonical scalar field on both sides of an inverted potential. It is shown that even though such an evolution is strongly non-slow roll, the resultant power spectrum is an exact power-law spectrum. Such solutions may therefore be useful for model-building on the string landscape. For that reason, we extend our analysis to inflation models which are characterized by non-canonical kinetic terms in chapters 5 and 6 (part 3). We show that there is a plethora of new inflation models that agree with observations. We perform non-canonical generalizations of simple inflation models and discover observational degeneracies among them. In light of this, we perform a flow analysis on a simulated Planck-precision data set to obtain constraints for the reconstruction of the inflationary potential from different classes of inflation models. Finally, chapter 7 constitutes the last part of this thesis which presents a brief summary and conclusions. All results are derived assuming that c = h = k B = 1. The analysis of canonical scalar fields in chapter 2 is presented in terms of the Planck mass, m Pl [approximate] 10 19 GeV, while the rest of the analysis is expressed in terms of the reduced Planck mass, M Pl = m Pl /[Special characters omitted.] <math> <f> <rad><rcd>8<g>p</g></rcd></rad></f> </math> . Even though this choice may add some complexity, it was done in order for our results to be consistent with the current literature. The metric signature for the Minkowski spacetime is taken to be η μν = diag(1,-1,-1,-1). Greek indices run from 0 to 3, while roman indices run from 1 to 3. The Einstein summation convention, where repeated indices are summed over, is used. We denote covariant derivatives by a semicolon and ordinary derivatives by a comma. Finally, derivatives with respect to the coordinate time, t , are denoted by overdots, whereas a prime denotes a derivative with respect to the conformal time, τ , or the scalar field, [straight phi] , depending on context.