PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CONTENTS 3.1.2 Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1.3 Comparison with the recent CMB observations . . . . . . . . . . . . . 46 3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2.1 The best fit background and inflationary parameters . . . . . . . . . 48 3.2.2 The spectra and the improvement in the fit . . . . . . . . . . . . . . . 49 3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4 Bi-spectra associated with local and non-local features 57 4.1 Models of interest and power spectra . . . . . . . . . . . . . . . . . . . . . . . 59 4.1.1 Inflationary potentials with a step . . . . . . . . . . . . . . . . . . . . 59 4.1.2 Oscillations in the inflaton potential . . . . . . . . . . . . . . . . . . . 60 4.1.3 Punctuated inflaton and the Starobinsky model . . . . . . . . . . . . 60 4.1.4 The power spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2 The scalar bi-spectrum in the Maldacena formalism . . . . . . . . . . . . . . 63 4.3 The numerical computation of the scalar bi-spectrum . . . . . . . . . . . . . 65 4.3.1 The contributions to the bi-spectrum on super-Hubble scales . . . . . 65 4.3.2 An estimate of the super-Hubble contribution to the non-Gaussianity parameter . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.3 Details of the numerical methods . . . . . . . . . . . . . . . . . . . . . 73 4.3.4 Comparison with the analytical results in the cases of power law inflation and the Starobinsky model . . . . . . . . . . . . . . . . . . . 76 4.4 Results in the equilateral limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5 The scalar bi-spectrum during preheating 85 5.1 Behavior of background and perturbations during preheating . . . . . . . . 87 5.1.1 Background evolution about a quadratic minimum . . . . . . . . . . 87 5.1.2 Evolution of the perturbations . . . . . . . . . . . . . . . . . . . . . . 92 5.2 The contributions to the bi-spectrum during preheating . . . . . . . . . . . . 98 5.2.1 The fourth and the seventh terms . . . . . . . . . . . . . . . . . . . . . 98 5.2.2 The second term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2.3 The remaining terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.2.4 The contribution to f NL during preheating . . . . . . . . . . . . . . . . 103 5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 xviii
CONTENTS 6 Effects of primordial features on the formation of halos 107 6.1 Models and comparison with the data . . . . . . . . . . . . . . . . . . . . . . 108 6.1.1 Comparison with the CMB and the LSS data . . . . . . . . . . . . . . 110 6.2 From the primordial spectrum to the formation rate of halos . . . . . . . . . 111 6.2.1 The matter power spectrum . . . . . . . . . . . . . . . . . . . . . . . . 111 6.2.2 Mass functions and the halo formation rates . . . . . . . . . . . . . . 112 6.3 The numerical methods: Essentials . . . . . . . . . . . . . . . . . . . . . . . . 113 6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.4.1 Joint constraints from the WMAP and the SDSS data . . . . . . . . . 114 6.4.2 Effects of features in the number density and the formation rate of halos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7 Imprints of primordial non-Gaussianity in the Ly-alpha forest 123 7.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 8 Summary and outlook 135 8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 xix
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: Contents 1 Introduction 1 1.1 The c
Page 23 and 24: List of Figures 1.1 A schematic tim
Page 25 and 26: Chapter 1 Introduction At a first g
Page 27 and 28: 2.725K. It is also found to be high
Page 29 and 30: 1.1. THE CONCORDANT, BACKGROUND COS
Page 31 and 32: 1.2. THE INFLATIONARY PARADIGM 1.2
Page 33 and 34: 1.2. THE INFLATIONARY PARADIGM log
Page 35 and 36: 1.2. THE INFLATIONARY PARADIGM wher
Page 37 and 38: 1.2. THE INFLATIONARY PARADIGM wher
Page 39 and 40: 1.2. THE INFLATIONARY PARADIGM The
Page 41 and 42: 1.2. THE INFLATIONARY PARADIGM yet
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
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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
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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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