PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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LIST OF FIGURES 4.4 The spectral dependence of the non-vanishing contributions to the bispectrum and the corresponding non-Gaussianity parameter in power law inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.5 The different contributions to the bi-spectrum in the case of the Starobinsky model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.6 The various contributions to the bi-spectrum in the different inflationary models of our interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.7 The non-Gaussianity parameter in the equilateral limit, viz. f eq , in the different inflationary models considered . . . . . . . . . . . . . . . . . . . . . . NL 83 5.1 The behavior of the scalar field and the first slow roll parameter during inflation and preheating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.2 The evolution of the second slow roll parameter during preheating . . . . . 90 5.3 The behavior of the curvature perturbation during preheating . . . . . . . . 97 5.4 The behavior of the quantity G 2 (k) during preheating . . . . . . . . . . . . . 101 6.1 The evolution of the first two slow roll parameters in inflationary potentials with a step and oscillatory terms . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.2 One and two dimensional constraints on the inflationary parameters . . . . 116 6.3 The scalar power spectrum for the models with local and non-local features 117 6.4 The theoretical matter power spectrum for the models with features plotted against the SDSS data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.5 The change in the number density and the formation rate of halos for the models with features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.1 The likelihood contours of the non-Gaussianity and the bias parameters f NL and b 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 xxiv
Chapter 1 Introduction At a first glance, the universe around us appears to be highly clumpy, with matter seemingly distributed in a rather non-uniform fashion. However, observations of millions of galaxies by different galaxy surveys such as the Two-degree-Field (2dF) galaxy redshift survey [1, 2] and the Sloan Digital Sky Survey (SDSS) [3, 4] indicate the universe to be homogeneous and isotropic on suitably large scales. These surveys suggest that the transition to homogeneity of the galaxy distribution occurs at length scales of around100 Mpc or so (in this context, see, for instance, Ref. [5]). On such large scales, it is General Relativity (GR) which is the theory that is expected to describe the universe. In GR, the fundamental quantity is the metric describing the spacetime, whose dynamics is determined by the matter through the Einstein field equations. The metric that describes the homogeneous and isotropic universe is referred to as the Friedmann-Lemaitre-Robertson-Walker (or, for convenience, simply Friedmann) line-element, which is essentially characterized by two quantities (see, for example, any of the following texts [6]). The first being the curvature of the spatial geometry of the universe, while the second is the scale factora(t), which allows one to account for the observed expansion of the universe. The quantity t denotes the cosmic time, i.e. the time as measured by clocks that are comoving with the expansion. The behavior of the scale factor a(t) is governed by the constituents of the universe through the Friedmann equations, which are the Einstein equations applied to the case of the Friedmann metric. A variety of observations point to the density of the universe today being rather close to the so-called critical density (with the dimensionless ratio of the actual density to the critical density deviating from unity by about one part in10 2 ), which corresponds to a geometry that is spatially rather flat. Till date, through different observations, we are aware of the fact that baryons (i.e. visible matter) and photons (viz. radiation) 1
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: List of Figures 1.1 A schematic tim
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Page 29 and 30: 1.1. THE CONCORDANT, BACKGROUND COS
Page 31 and 32: 1.2. THE INFLATIONARY PARADIGM 1.2
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Page 35 and 36: 1.2. THE INFLATIONARY PARADIGM wher
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Page 39 and 40: 1.2. THE INFLATIONARY PARADIGM The
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Page 43 and 44: 1.3. THE GENERATION AND IMPRINTS OF
Page 45 and 46: 1.5. THE FORMATION OF THE LARGE SCA
Page 47 and 48: 1.7. NOTATIONS AND CONVENTIONS resu
Page 49 and 50: Chapter 2 Generation of localized f
Page 51 and 52: 2.1. THE INFLATIONARY MODELS OF INT
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
Page 63 and 64: 2.4. THE SCALAR AND THE CMB ANGULAR
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
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3.2. RESULTS 0.2 0.15 0.1 ∆ χ 2
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3.2. RESULTS 7000 150 6000 100 50 l
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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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