PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 2. GENERATION OF LOCALIZED FEATURES tive of attempting to constrain the models from the data, because only a more restricted class of inflationary models can be expected to provide an improved fit to these outliers. Therefore, it is a worthwhile exercise to systematically explore models that lead to specific deviations from the standard power law, inflationary perturbation spectrum, and also provide an improved fit to the data. Various efforts towards a model independent reconstruction of the primordial spectrum from the observed pattern of the CMB anisotropies seem to indicate the presence of certain features in the spectrum [69]. (However, we should add that there also exist other views on the possibility of features in the primordial spectrum; in this context, see, for example, Refs. [70].) In particular, a burst of oscillations in the primordial spectrum seems to provide a better fit to the CMB angular power spectrum near the multipole moments of l = 22 and 40. Generating these oscillations requires a short period of deviation from slow roll inflation [71, 72], and such a departure has often been achieved by introducing a small step in the popular, quadratic potential describing the canonical scalar field (see Refs. [73, 74, 75]; for a discussion on other models, see, for instance, Refs. [76, 77]). At the cost of three additional parameters which characterize the location, the height and the width of the step, it has been found that this model provides a considerably better fit to the CMB data with the least squares parameterχ 2 eff typically improving by about7, when compared to the nearly scale invariant spectrum that would have resulted in the absence of the step [74, 75]. But, such a chaotic inflation model leads to a reasonable amount of tensors, and these models will be ruled out if tensors are not detected corresponding to a tensor-to-scalar ratio of, say, r ≃ 0.1. Our aims in this chapter are twofold. Firstly, we wish to examine whether, with the introduction of a step, other inflationary models too perform equally well against the CMB data, as the quadratic potential does. Secondly, we would also like to consider a model that leads to a tensor-to-scalar ratio of r < 0.1, so that suitable alternative models exist if the tensor contribution turns out to be smaller. Motivated by these considerations, apart from revisiting the popular quadratic potential, we shall investigate the effects of the step in a small field model (in this context, see, for example, Ref. [78]) and a tachyon model [79]. Also, with possible applications to future datasets in mind (such as the ongoing Planck mission [20]), we shall evaluate the tensor power spectrum exactly, and include its contribution in our analysis. We shall compare the models with the CMB data from the WMAP, QUaD and ACBAR missions. We shall consider the five as well as the seven-year WMAP data [18, 19], the QUaD June 2009 data [11] and the ACBAR 2008 data [13] to arrive at the observational constraints on the inflationary parameters. We find 26
2.1. THE INFLATIONARY MODELS OF INTEREST that, as one may expect, a step at a suitable location and of a certain magnitude and width improves the fit to the outliers (near l = 22 and 40) in all the cases. We point out that, if the amplitude of the tensors prove to be small, the quadratic potential and the tachyon model will become inviable, and we will have to turn our attention to examples such as the small field models. This chapter is organized as follows. In the following section, we shall outline the different inflationary models that we shall be focusing on. In Section 2.2, we shall discuss the methodology that we adopt for comparing the inflationary models with the data, the datasets that we use for our analysis, and the priors on the various parameters that we work with. In Section 2.3, we shall present the results of our comparison of the theoretical CMB angular power spectra that arise from the various models with the WMAP five-year as well as seven-year data, the QUaD and the ACBAR data. We shall tabulate the best fit values that we obtain on the background cosmological parameters and the parameters describing the inflationary models. We shall also illustrate the constraints that we arrive at on the parameters describing the step in the case of the small field model. Further, we shall explicitly show that the models with the step perform better against the data because of the fact that they lead to an improvement in the fit to the outliers around l = 22 and 40. In Section 2.4, we shall illustrate the scalar power spectra and the CMB angular power spectra corresponding to the best fit values of the parameters of some of the models that we consider. Finally, in Section 2.5, we shall close with a brief summary, and a few comments on certain implications of our results. 2.1 The inflationary models of interest In this section, we shall list the different inflationary models that we shall consider, and briefly outline the parameters involved in each of these cases. 2.1.1 The power law case Recall that, the conventional power law, scalar and tensor spectra are given by Eqs. (1.24). We shall treat this power law case as our reference model with respect to which we shall compare the performance of the other models against the data. Often, when comparing the power law case with the observations, the following slow roll consistency condition is further assumed: r = −8n T [11, 13, 18, 19]. But, we shall not impose this condition so that, while comparing the power law case with the data, we shall work with all the four 27
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 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
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: Chapter 2 Generation of localized f
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 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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4.3. THE NUMERICAL COMPUTATION OF T
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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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