PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 5. THE SCALAR BI-SPECTRUM DURING PREHEATING the post-inflationary dynamics (that is to say preheating instabilities) can modify it. In the same manner, it is tempting to conjecture that the scalar bi-spectrum calculated at the end of multi-field inflation will not necessarily be the same as the one observed in the data [125]. In particular, the so-called consistency relations [52], which relate the three-point and the four-point correlation functions (or, equivalently, the corresponding dimensionless non-Gaussianity parameters f NL and τ NL ) might receive corrections in a multi-field context due to metric preheating. 106
Chapter 6 Effects of primordial features on the formation of halos As we had described in the introductory chapter, apart from the CMB, the LSS data too are expected to provide constraints on the pattern as well as the characteristics of the primordial perturbations. Any significant change in the primordial scalar power spectrum will correspondingly modify the matter power spectrum [cf. Eq. (1.30)] evaluated today. Hence, the features in the inflationary scalar perturbation spectrum that we had discussed extensively in Chapters 2 and 3, in addition to their imprints on the CMB, will affect the matter power spectrum which, in turn, will leave its signatures on the formation rates of the dark matter halos. In fact, the effects of steps or oscillations in the inflaton potential on the predicted number of halos was investigated recently [126]. The analysis was carried out with the inflationary perturbation spectrum evaluated using the slow roll approximation. But, the slow roll parameters can turn large in the presence of steps or oscillatory terms in the inflationary potentials and, as a result, the power spectrum evaluated in the slow roll approximation can differ considerably from the actual power spectrum. Moreover, with the ever increasing quality of the LSS observations, in particular, the halo power spectrum constructed using the Luminous Red Galaxies (LRG) from the seventh data release (DR7) of SDSS [3, 4], it may be a worthwhile exercise to actually compare the models with the available data to arrive at additional constraints on the primordial features that we had considered in the preceding chapters. With the above points in mind, in this chapter, we shall utilize the code that we have developed to compute the inflationary perturbation spectrum (cf. Section 4.3.3) and, thereby, evaluate the corresponding matter power spectrum and the number of halos formed. We shall compute the number densities and the formation rates of halos in the 107
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Primordial features and non-Gaussia
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Declaration This thesis is a presen
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Acknowledgments According to a popu
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Abstract Currently, inflation is th
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ABSTRACT tensors prove to be small
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ABSTRACT the best fit values arrive
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Contents 1 Introduction 1 1.1 The c
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CONTENTS 6 Effects of primordial fe
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List of Figures 1.1 A schematic tim
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Chapter 1 Introduction At a first g
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2.725K. It is also found to be high
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1.1. THE CONCORDANT, BACKGROUND COS
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1.2. THE INFLATIONARY PARADIGM 1.2
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1.2. THE INFLATIONARY PARADIGM log
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1.2. THE INFLATIONARY PARADIGM wher
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1.2. THE INFLATIONARY PARADIGM wher
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1.2. THE INFLATIONARY PARADIGM The
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1.2. THE INFLATIONARY PARADIGM yet
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1.3. THE GENERATION AND IMPRINTS OF
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1.5. THE FORMATION OF THE LARGE SCA
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1.7. NOTATIONS AND CONVENTIONS resu
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Chapter 2 Generation of localized f
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2.1. THE INFLATIONARY MODELS OF INT
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2.2. METHODOLOGY, DATASETS, AND PRI
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2.2. METHODOLOGY, DATASETS, AND PRI
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2.3. BOUNDS ON THE PARAMETERS 2.3 B
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2.3. BOUNDS ON THE PARAMETERS Model
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2.4. THE SCALAR AND THE CMB ANGULAR
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2.4. THE SCALAR AND THE CMB ANGULAR
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2.5. DISCUSSION by the canonical sc
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Chapter 3 Non-local features in the
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3.1. MODELS AND METHODOLOGY on the
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3.1. MODELS AND METHODOLOGY values
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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
Page 79 and 80: 3.3. DISCUSSION WMAP as well as the
Page 81 and 82: Chapter 4 Bi-spectra associated wit
Page 83 and 84: 4.1. MODELS OF INTEREST AND POWER S
Page 85 and 86: 4.1. MODELS OF INTEREST AND POWER S
Page 87 and 88: 4.2. THE SCALAR BI-SPECTRUM IN THE
Page 89 and 90: 4.3. THE NUMERICAL COMPUTATION OF T
Page 105 and 106: 4.4. RESULTS IN THE EQUILATERAL LIM
Page 107 and 108: 4.4. RESULTS IN THE EQUILATERAL LIM
Page 109 and 110: Chapter 5 The scalar bi-spectrum du
Page 111 and 112: 5.1. BEHAVIOR OF BACKGROUND AND PER
Page 123 and 124: 5.2. THE CONTRIBUTIONS TO THE BI-SP
Page 129: 5.3. DISCUSSION significant during
Page 133 and 134: 6.1. MODELS AND COMPARISON WITH THE
Page 135 and 136: 6.2. FROM THE PRIMORDIAL SPECTRUM T
Page 137 and 138: 6.3. THE NUMERICAL METHODS: ESSENTI
Page 139 and 140: 6.4. RESULTS Model Quadratic Quadra
Page 141 and 142: 6.4. RESULTS 6e-09 Quadratic potent
Page 143 and 144: 6.4. RESULTS 30 4 20 Change in R Ch
Page 145 and 146: 6.5. DISCUSSION wherein one works w
Page 147 and 148: Chapter 7 Imprints of primordial no
Page 149 and 150: 7.1. FORMALISM and the LSS studies.
Page 151 and 152: 7.1. FORMALISM only mildly non-line
Page 153 and 154: 7.1. FORMALISM If the bi-spectrum c
Page 155 and 156: 7.2. RESULTS 0.12 0.13 2e3 , 2.2e3
Page 157 and 158: 7.3. CONCLUSIONS 7.3 Conclusions To
Page 159 and 160: Chapter 8 Summary and outlook In th
Page 161 and 162: 8.2. OUTLOOK factorily [69, 70]. Ra
Page 163 and 164: Bibliography [1] See,http://magnum.
Page 165 and 166: BIBLIOGRAPHY [27] See,http://cfht.h
Page 167 and 168: BIBLIOGRAPHY [55] F. Arroja, A. E.
Page 169 and 170: BIBLIOGRAPHY [77] R. K. Jain, P. Ch
Page 171 and 172: BIBLIOGRAPHY [103] R. Allahverdi, J
Page 173 and 174: BIBLIOGRAPHY [132] S. Sasaki, Publ.
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PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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