PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 6. EFFECTS OF PRIMORDIAL FEATURES ON THE FORMATION OF HALOS 100000 1000 Quadratic potential Quadratic potential with a step Quadratic potential with sinusoidal modulation Axion monodromy model P M (k)h −3 Mpc 3 1 10000 1000 0.01 0.1 0.001 0.0001 0.01 1 100 khMpc −1 Figure 6.4: The best fit matter power spectrum P M (k) corresponding to the different inflationary scalar power spectra we had plotted in the earlier figure. The inset highlights the imprints of the primordial features on the matter power spectrum in the domain where the baryon acoustic oscillations also play a role. The black dots with bars corresponds to the power spectrum data from SDSS obtained upon combining main galaxies and the LRGs with error bars arrived at from the diagonal elements of the corresponding covariance matrix. It should be noted that, since we have plotted the linear power spectrum, without taking into account the non-linear effects, the theoretical best fit curves are unable to fit the data for k > 0.1hMpc −1 . potential. In order to arrive at the maximum possible change in the number density of halos when compared to the conventional nearly scale invariant primordial spectrum, for the models with oscillations in the potential, we have chosen values for the parametersαand β that lie within2-σ from the best fit values. We have chosen the parameters in such a way that they create the largest deviation from the nearly scale invariant power spectra that are allowed by the CMB and the LSS data. In Figure 6.5, apart from the results for the best fit values, we have plotted the number density and the formation rates of halos for the cases wherein[α,ln(β/M Pl )] is set to(2×10 −3 ,−1.7) and(2×10 −4 ,−3.5) for the quadratic potential with the sinusoidal modulations and the axion monodromy model, respectively. 118
6.4. RESULTS 30 4 20 Change in R Changein dn ST /dlnM 2 0 -2 Changein R -20 Sine model best fit Sine model best fit -4 Monodromy model best fit Monodromy model best fit -30 3 20 2 10 1 0 0 -1 -10 -2 -3 10000 1e+06 1e+08 1e+10 1e+12 1e+14 10000 1e+06 1e+08 1e+10 1e+12 1e+14 M/M ⊙ Change in dn ST /dlnM 10 0 -10 M/M ⊙ Figure 6.5: The percentage change in the formation rate of halos (in the Press-Schechter formalism, on top) and in their number density (in the Sheth-Tormen formalism, at the bottom) for the two inflationary models containing oscillatory terms with respect to the more conventional quadratic potential. The figures on the left correspond to the best fit values, while those on the right correspond to values chosen within the 2-σ confidence contours of the parameters α and β, determined from the joint constraints of the WMAP and SDSS data, as shown in Figure 6.2. In order to highlight the effects due to the primordial features, we have frozen the background parameters at the best fit values arrived at when the primordial spectrum is determined by the quadratic potential. We have then worked with the best fit values for the potential parameters to arrive at the figures on the left. We have plotted the percentage change in logarithmic mass bins, i.e.∆log 10 (M/M ⊙ ), of 0.2. It is clear that the features corresponding to the best fit values do not lead any substantial difference in either the number or the formation rates of the halos. However, note that the quadratic potential with superimposed sinusoidal oscillations leads to a20% change in the number of halos formed when we choose to work with values of α and β that lie within the 2-σ contours. In arriving at the plots, we have fixed the values of the parametermandλat their best fit values as shown in the Table 6.2, since these parameters do not play a role in altering the features in the spectrum. We have also chosen the value of δ to be the best fit value for both the models. It is evident from the figure that, for the best fit values of the parameters, the change in the number density is completely negligible (∼ 2%). However, we find 119
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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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Page 109 and 110: Chapter 5 The scalar bi-spectrum du
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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
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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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