PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 1. INTRODUCTION Figure 1.1: An artist’s rendering of the timeline of the universe, from the big bang through the epochs of inflation, decoupling, dark ages and the formation of structure, till the current accelerated expansion driven by dark energy. (Image courtesy: NASA/WMAP Science Team.) to the formation of the LSS and the present epoch of accelerated expansion driven by dark energy—that we have outlined above. The aims of this thesis, as we have outlined in the abstract, can be largely said to be twofold. Often in the literature, while considering models of inflation, attention is restricted to models which permit only slow roll. We shall instead focus on models that lead to deviations from slow roll, which result in specific features in the inflationary scalar perturbation spectrum. These features, not only lead to an improved fit to the observed CMB angular power spectrum, but, interestingly, as we shall illustrate, they also produce larger levels of non-Gaussianities, as is possibly suggested by the recent analysis of the WMAP data. As a related issue, we shall also discuss the extent of the contribution to the bi-spectrum due to the epoch of preheating that immediately succeeds the inflationary 4
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 5
Page 1: Primordial features and non-Gaussia
Page 5: Declaration This thesis is a presen
Page 9 and 10: Acknowledgments According to a popu
Page 11 and 12: Abstract Currently, inflation is th
Page 13 and 14: ABSTRACT tensors prove to be small
Page 15 and 16: ABSTRACT the best fit values arrive
Page 17 and 18: Contents 1 Introduction 1 1.1 The c
Page 19: CONTENTS 6 Effects of primordial fe
Page 23 and 24: List of Figures 1.1 A schematic tim
Page 25 and 26: Chapter 1 Introduction At a first g
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Page 49 and 50: Chapter 2 Generation of localized f
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Page 53 and 54: 2.2. METHODOLOGY, DATASETS, AND PRI
Page 55 and 56: 2.2. METHODOLOGY, DATASETS, AND PRI
Page 57 and 58: 2.3. BOUNDS ON THE PARAMETERS 2.3 B
Page 59 and 60: 2.3. BOUNDS ON THE PARAMETERS Model
Page 61 and 62: 2.4. THE SCALAR AND THE CMB ANGULAR
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Page 65 and 66: 2.5. DISCUSSION by the canonical sc
Page 67 and 68: Chapter 3 Non-local features in the
Page 69 and 70: 3.1. MODELS AND METHODOLOGY on the
Page 71 and 72: 3.1. MODELS AND METHODOLOGY values
Page 73 and 74: 3.2. RESULTS Datasets WMAP-7 WMAP-7
Page 75 and 76: 3.2. RESULTS 0.2 0.15 0.1 ∆ χ 2
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3.3. DISCUSSION WMAP as well as the
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Chapter 4 Bi-spectra associated wit
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4.1. MODELS OF INTEREST AND POWER S
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4.1. MODELS OF INTEREST AND POWER S
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4.2. THE SCALAR BI-SPECTRUM IN THE
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4.3. THE NUMERICAL COMPUTATION OF T
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4.4. RESULTS IN THE EQUILATERAL LIM
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4.4. RESULTS IN THE EQUILATERAL LIM
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Chapter 5 The scalar bi-spectrum du
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5.1. BEHAVIOR OF BACKGROUND AND PER
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5.2. THE CONTRIBUTIONS TO THE BI-SP
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5.3. DISCUSSION significant during
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Chapter 6 Effects of primordial fea
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6.1. MODELS AND COMPARISON WITH THE
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6.2. FROM THE PRIMORDIAL SPECTRUM T
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6.3. THE NUMERICAL METHODS: ESSENTI
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6.4. RESULTS Model Quadratic Quadra
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6.4. RESULTS 6e-09 Quadratic potent
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6.4. RESULTS 30 4 20 Change in R Ch
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6.5. DISCUSSION wherein one works w
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Chapter 7 Imprints of primordial no
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7.1. FORMALISM and the LSS studies.
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7.1. FORMALISM only mildly non-line
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7.1. FORMALISM If the bi-spectrum c
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7.2. RESULTS 0.12 0.13 2e3 , 2.2e3
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7.3. CONCLUSIONS 7.3 Conclusions To
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Chapter 8 Summary and outlook In th
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8.2. OUTLOOK factorily [69, 70]. Ra
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Bibliography [1] See,http://magnum.
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BIBLIOGRAPHY [27] See,http://cfht.h
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BIBLIOGRAPHY [55] F. Arroja, A. E.
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BIBLIOGRAPHY [77] R. K. Jain, P. Ch
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BIBLIOGRAPHY [103] R. Allahverdi, J
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BIBLIOGRAPHY [132] S. Sasaki, Publ.
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PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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