PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 2. GENERATION OF LOCALIZED FEATURES Models Parameter Lower limit Upper limit ln (10 10 A S ) 2.7 4.0 Power law n S 0.5 1.5 case r 0.0 1.0 n T −0.5 0.5 ln ( ) 10 10 m 2 /M 2 −0.77 −0.58 Pl Quadratic model d 1.3×10 −3 1.7×10 −3 with a step φ 0 /M Pl 13.0 15.0 ∆φ/M Pl 0.015 0.03 ln ( ) 10 10 V 0 /M 4 1.50 1.86 Pl Small field model −d 1.0×10 −4 2.0×10 −4 with a step φ 0 /M Pl 7.8 8.1 ∆φ/M Pl 5.0×10 −3 1.0×10 −2 ln (10 10 φ ∗ /M Pl ) 34.506 34.518 Tachyon model −d 1.3×10 −3 1.9×10 −3 with a step φ 0 /M Pl 7.81×10 5 7.83×10 5 ∆φ/M Pl 340 410 Table 2.1: The priors on the various parameters that describe the primordial spectrum in the power law case, and the inflationary potential in all the other cases. We work with these priors when comparing the models with all the datasets. 32
2.3. BOUNDS ON THE PARAMETERS 2.3 Bounds on the background and the inflationary parameters In this section, we shall present the results of our analysis. As we mentioned above, we have separately compared the models with the WMAP five-year and seven-year data. We have also compared the models with the WMAP five-year data along with the QUaD data, and with the QUaD as well as the ACBAR data. We shall tabulate below the best fit values that we arrive at on the various background and inflationary parameters for the power law case and for the inflationary models with the step. We shall also provide the least squares parameter χ 2 eff in all the cases, viz. the power law case and the three inflationary models, with and without the step. 2.3.1 The best fit values and the effective least squares parameterχ 2 eff In Tables 2.2 and 2.3, we have listed the best fit values for the various parameters in the power law case and in the three inflationary models with the step. These tables contain the results that we arrive at upon comparing the models with the WMAP five-year (denoted as WMAP-5) and seven-year (denoted as WMAP-7) data, the QUaD as well as the ACBAR data sets. Note that we have only presented the results for the power law case, and when the step (2.5) has been introduced in the quadratic potential (2.1), the small field model (2.2) and the tachyon model (2.4). We find that the values we have obtained upon comparing the power law case with the WMAP five and seven-year data and the QUaD and the ACBAR data match well with the results quoted by the WMAP [18, 19] and the QUaD teams [11]. Also, the results for the quadratic potential with the step agree well with the results quoted in the recent work [75]. In Table 2.4, we have listed the least squares parameter χ 2 eff for all the different models and datasets of our interest. It is clear from the table that the presence of the step leads to a reduction in χ 2 eff by about 7-9 in all the three inflationary models that we have considered. Also, note that such an improvement is achieved in all the datasets that we have compared the models with. When we compare the contribution to theχ 2 eff at the low multipoles (i.e. up to l = 32, see Refs. [18, 19]) from the output of the WMAP likelihood code for, say, the WMAP seven-year data, we find that the introduction of the step in the inflaton potential reduces the χ 2 eff for the TT data over this range by about 5-6 in all the cases. In Figure 2.1, we have plotted the difference in χ 2 eff with and without the step, as a function of the multipoles whenl > 32, for the WMAP seven-year data. We have plotted 33
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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 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
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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: 2.2. METHODOLOGY, DATASETS, AND PRI
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
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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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