PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 3. NON-LOCAL FEATURES IN THE PRIMORDIAL SPECTRUM Datasets Model WMAP-7 WMAP-7+ACT Power law case 7468.4 7500.4 Chaotic model with 7468.0 7498.2 sinusoidal modulation Axion monodromy model 7455.3 7495.2 Table 3.3: The χ 2 eff for the different models and datasets that we have considered. Note that we have used the Gibbs approach in the WMAP likelihood code to calculate the χ 2 eff for the CMB TT spectrum at the low multipoles (i.e. for l < 32) [18, 19]. better when the small scale data from ACT is included suggests that oscillations can be favored by the data. Secondly, oscillations of fixed amplitude in the potential as in the monodromy model seem to be more favored by the data than the oscillations of varying amplitude as in the case of the chaotic model with sinusoidal modulations. In fact, this strengthens similar conclusions that has been arrived at earlier [94, 95], wherein Planck scale oscillations of a certain amplitude in the primordial spectrum was found to lead to a considerably better fit to the data. It is now interesting to enquire as to whether there exist localized windows of multipoles over which the improvement in the fit occurs. We find that, in the case of the chaotic model with sinusoidal modulations, as far as the WMAP seven-year data is concerned, there is an improvement of at most unity in all the multipoles combined. In Figure 3.1, after binning suitably, we have plotted the difference∆χ 2 eff = χ2 eff (model)−χ2 eff (power law) as a function of the multipoles for the WMAP seven-year TT and TE data in the case of the axion monodromy model. It is clear from the figure that the source of the improvement in the fit is not confined to any specific set of multipoles, and it arises due to small increments that accrue over the entire range of available data. In Figures 3.2 and 3.3, we have plotted the scalar power spectra and the corresponding CMB TT angular power spectra for the best fit values of the WMAP seven-year data in the two inflationary models that we have considered. 50
3.2. RESULTS 0.2 0.15 0.1 ∆ χ 2 eff (TT) 0.05 0 -0.05 -0.1 -0.15 200 400 600 800 1000 1200 l 0.02 0.01 0 -0.01 -0.02 ∆ χ 2 eff (TE) -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 100 200 300 400 500 600 700 800 Figure 3.1: The difference in χ 2 eff with respect to the reference model, i.e. ∆χ2 eff = χ 2 eff (model)−χ2 eff (power law)], in the case of the axion monodromy model has been plotted as a function of the multipole moment for the WMAP seven-year data, after binning in the multipole space with l bin = 10. While the figure on top corresponds to the WMAP seven-yearTT data (for l > 32), the lower one is for the TE data (for l > 24). l 51
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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
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
Page 69 and 70: 3.1. MODELS AND METHODOLOGY on the
Page 71 and 72: 3.1. MODELS AND METHODOLOGY values
Page 73: 3.2. RESULTS Datasets WMAP-7 WMAP-7
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 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
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5.2. THE CONTRIBUTIONS TO THE BI-SP
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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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