PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 6. EFFECTS OF PRIMORDIAL FEATURES ON THE FORMATION OF HALOS inflationary models with the step and oscillations that we had considered in Chapters 2 and 3. Our goal will be to estimate the maximum possible change in the number density and the formation rate of halos in these models, when compared with, say, inflation driven by the simplest quadratic potential. In order to arrive at the parameter space of interest, we shall compare the models with the CMB as well as the LSS data. Towards this end, we shall make use of the WMAP seven-year (WMAP-7) data [19] and the LRG halo power spectrum data from SDSS DR7 [4]. We find that the power spectra with features that correspond to the best fit values of the inflationary parameters do not typically lead to substantial deviations in the formation rates of halos. However, we find that, in certain models that we consider, the potential parameters that lie within2-σ of the best fit values obtained from the joint constraints of WMAP and SDSS can lead to a 20% change in the number of halos formed for halo masses ranging over 10 4 –10 14 M ⊙ . This chapter is organized as follows. In the following section, we shall quickly list the inflationary models of our interest, which lead to specific features in the primordial scalar power spectrum. We shall also outline the method that we adopt to compare the models with the data. In Section 6.2, we shall describe the formalism to arrive at the halo formation rate from the inflationary power spectra. In Section 6.3, we shall provide a few essential details concerning the numerical procedures that we follow. We shall discuss the results in Section 6.4, and we shall close with a few concluding remarks regarding the implications of our results in Section 6.5. 6.1 Models and comparison with the data In this section, we shall quickly discuss the inflationary models of our interest and the scalar power spectra produced by them. We shall work with the simplest case of inflation driven by the canonical scalar field. We shall treat the conventional quadratic potential (2.1) to be our reference model. We shall consider features generated due to the step (2.5) introduced in the quadratic potential, and the potentials (3.1) and (3.2) which contain oscillatory terms. As we have discussed earlier, these models result in features that lead to an improved fit to the CMB data. In Figure 6.1, we have plotted the behavior of the first two slow roll parameters in these models. As we have emphasized before, it is the deviations from slow roll seen in the figure that lead to features in the scalar power spectra. 108
6.1. MODELS AND COMPARISON WITH THE DATA 1 0.8 Quadratic potential Quadratic potential with a step Quadratic potential with sinusoidal modulation Axion monodromy model 0.015 0.6 ǫ1 0.4 0.01 0.2 0.005 0 0.001 14 15 16 5 20 35 50 65 3 N 6.0 0 ǫ2 3.0 -3 14 15 16 0.0 -3.0 5 20 35 50 65 N Figure 6.1: Evolution of first two slow roll parameters ǫ 1 and ǫ 2 have been plotted as a function of the number of e-folds N for the quadratic potential without and with the step (the black and the red curves, respectively), the quadratic potential superimposed by sinusoidal modulations (the green curve) and the axion monodromy model (the blue curve). The curves have been plotted for potential parameters that lead to the best fit to the recent CMB and LSS data. In the quadratic potential without the step, as is well known, the field continues to roll slowly until the end of inflation, whereas, when the step is introduced, it briefly deviates from slow roll around the time the field crosses the step. In the case of the potentials with oscillations, for the best fit values, the axion monodromy model leads to strong departures from slow roll, with ǫ 2 turning ‘large’ repeatedly, right till the termination of inflation. The insets provide a closer view of the behavior of the slow roll parameters over a smaller range of e-folds. 109
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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
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2.2. METHODOLOGY, DATASETS, AND PRI
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2.3. BOUNDS ON THE PARAMETERS 2.3 B
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2.3. BOUNDS ON THE PARAMETERS Model
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2.4. THE SCALAR AND THE CMB ANGULAR
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2.4. THE SCALAR AND THE CMB ANGULAR
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2.5. DISCUSSION by the canonical sc
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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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Page 87 and 88: 4.2. THE SCALAR BI-SPECTRUM IN THE
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Page 131: Chapter 6 Effects of primordial fea
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
Page 157 and 158: 7.3. CONCLUSIONS 7.3 Conclusions To
Page 159 and 160: Chapter 8 Summary and outlook In th
Page 161 and 162: 8.2. OUTLOOK factorily [69, 70]. Ra
Page 163 and 164: Bibliography [1] See,http://magnum.
Page 165 and 166: BIBLIOGRAPHY [27] See,http://cfht.h
Page 167 and 168: BIBLIOGRAPHY [55] F. Arroja, A. E.
Page 169 and 170: BIBLIOGRAPHY [77] R. K. Jain, P. Ch
Page 171 and 172: BIBLIOGRAPHY [103] R. Allahverdi, J
Page 173 and 174: BIBLIOGRAPHY [132] S. Sasaki, Publ.
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PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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