PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 4. BI-SPECTRA ASSOCIATED WITH LOCAL AND NON-LOCAL FEATURES 1e-16 1e-20 1e-24 1e-28 1e-32 Punctuated inflation 1e-14 k 6 |Gn(k)| 1e-16 1e-18 1e-20 Quadratic potential with a step 1e-12 1e-15 1e-18 1e-21 Axion monodromy model 1e-24 1e-05 0.0001 0.001 0.01 k Figure 4.6: The set of quantitiesk 6 |G n (k)| plotted as in the previous figure with the same choice of colors to represent the different G n (k). The figures on top, in the middle and at the bottom correspond to punctuated inflation, the quadratic potential with a step and the axion monodromy model, respectively, and they have been plotted for values of the parameters that lead to the best fit to the WMAP data [77, 85, 101]. In the middle figure, the dashed lines correspond to the quadratic potential when the step is not present. 82
4.4. RESULTS IN THE EQUILATERAL LIMIT 1e+05 3 1e+03 0 |f eq | NL 10 -3 0.001 0.01 0.1 0.001 Punctuated inflation Starobinsky model 1e-05 0.0001 0.001 0.01 4 2 f eq NL 0 -2 -4 Quadratic potential with a step Small field model with a step 1e-05 0.0001 0.001 0.01 0.1 1600 800 f eq NL 0 -800 -1600 Axion monodromy model 1e-05 0.0001 0.001 0.01 k Figure 4.7: A plot of f eq corresponding to the various models that we have considered. NL The figure at the top contains the absolute value off eq , plotted on a logarithmic scale (for NL convenience in illustrating the extremely large values that arise), in the Starobinsky model and the punctuated inflationary scenario. The inset highlights the growth in f eq at large NL wavenumbers in the case of the Starobinsky model, in conformity with the conclusions that have also been arrived at analytically [55]. The figure in the middle contains f eq for NL the cases wherein a step has been introduced in a quadratic potential and a small field model. The figure at the bottom corresponds to that of the axion monodromy model. As we had mentioned before, these sets of models lead to scalar power spectra with certain common characteristics. Needless to say, while f eq is considerably different in the first NL and the last sets of models, it is almost the same in the case of models with a step. These similarities and differences can be attributed completely to the background dynamics. 83
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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
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
Page 75 and 76: 3.2. RESULTS 0.2 0.15 0.1 ∆ χ 2
Page 77 and 78: 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: 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 and 130: 5.3. DISCUSSION significant during
Page 131 and 132: Chapter 6 Effects of primordial fea
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
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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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