PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 6. EFFECTS OF PRIMORDIAL FEATURES ON THE FORMATION OF HALOS that, for the case of the quadratic potential with sinusoidal modulation, the numbers can change by as much as 20% for values of the potential parameters α and β that lie within 2-σ. It should also be highlighted that the monodromy model does not seem to lead to the same extent of change in the number density and the rate of formation of halos, despite the fact that it produces fine oscillations in the primordial as well as the linear matter power spectra (cf. Figures 6.3 and 6.4). Actually, while the unbinned number density does indicate a 5-15% change, we find that, the change proves to be smaller when we bin the numbers in logarithmic mass bins, i.e.∆log 10 (M/M ⊙ ), of0.2. Evidently, binning seems to average out the rapid oscillations, resulting in a smaller extent of change in the numbers. 6.5 Discussion In this chapter, we have investigated the effects of primordial features on the matter power spectrum as well as the number of halos formed and their rate of formation. Similar work in this context [126] had suggested that a small change in the parameters describing the inflaton potential would lead to a drastic change in the number of halos formed. The earlier results and conclusions had been arrived at based on the inflationary perturbation spectrum evaluated using the slow roll approximation. In contrast, we have carried a complete and accurate numerical analysis. Further, we have made use of the Sheth-Tormen mass function (instead of the older Press-Schechter one) which is known to fit the data from the N-body simulations better. We have included the baryon acoustic oscillations in our analysis to have a more realistic comparison. Moreover, we have explicitly compared the potentials we have considered with the WMAP-7 and SDSS LRG DR7 datasets to arrive at the parameter space of interest. We find that, the best fit values for the potential parameters (with the background parameters kept fixed) lead to hardly any change in the number of halos formed when compared to the conventional quadratic potential that generates a nearly scale invariant primordial spectrum. However, partly consistent with the earlier result, we find that values for the potential parameters that lie within2-σ of the best fit values indeed lead to a reasonable change in the number of halos formed and in the formation rate. For instance, we find that, with superimposed sinusoidal modulations, the quadratic potential leads to as much as a 20% change in the halo number density and the rate of formation [135]. Needless to mention, the step of comparing the models against the data is crucial as this imposes real bounds on the extent of changes in the numbers involved. It is worthwhile to note that the inclusion of SDSS data reduces the maximum change in number density by about 10%, when compared to case 120
6.5. DISCUSSION wherein one works with the parameters constrained by the WMAP data alone. We would like to close this chapter with the following remarks. As we had pointed out before, while comparing with the SDSS data, we have not taken into account the nonlinear effects on the matter power spectrum. It is for this reason that the theoretical curve had not fit the observational data well on small scales (cf. Figure 6.4). Clearly, a more complete analysis would involve modeling of the non-linear effects and their inclusion in evaluating the matter power spectrum [127]. For instance, it will be interesting to compare the results on the number of haloes formed in numerical simulations, evolved from primordial spectra with features, with the small scale data. 121
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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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Chapter 4 Bi-spectra associated wit
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4.1. MODELS OF INTEREST AND POWER S
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4.1. MODELS OF INTEREST AND POWER S
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4.2. THE SCALAR BI-SPECTRUM IN THE
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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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Page 105 and 106: 4.4. RESULTS IN THE EQUILATERAL LIM
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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: 6.4. RESULTS 30 4 20 Change in R Ch
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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