PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 6. EFFECTS OF PRIMORDIAL FEATURES ON THE FORMATION OF HALOS and equal to unity in the early matter dominated epoch, i.e. at a sufficiently high redshift of, say, z ≃ 30 [18, 133]. After having obtained the matter power spectrum, we calculate the variance σ(R) using Eq. (6.3). The integral can be evaluated numerically with the simplest of algorithms, provided the power spectrum proves to be smooth and devoid of any features. In contrast, when these exist features such as repeated oscillations, certain care is required, and we have made use of an adaptive integration routine to compute the integral involved [107]. We have carried out the integral from a suitably small mode (such as k = 10 −5 Mpc −1 ) up to a mode where the window function cuts off the integrand. Finally, we obtain at the quantity dlnσ/dlnM by numerical differentiation. We should stress here that, keeping in mind the presence of oscillations in the power spectra, we have computed σ anddlnσ/dlnM with care and high accuracy. We should also add that we have cross checked our result by fitting the numerical values of σ(R) to the Chebyshev polynomials and calculating the corresponding derivative from the polynomial (in this context, see Ref. [133]). 6.4 Results In this section, we shall present the results of our comparison of the models of our interest with the CMB and the LSS data. We shall also discuss the effects of primordial spectra with features on the formation of halos. 6.4.1 Joint constraints from the WMAP and the SDSS data In Table 6.2 below, we have tabulated the best fit values of the background and the potential parameters obtained from the MCMC analysis using the WMAP-7 and the SDSS LRG DR7 data. We have also listed the effective least squared parameter χ 2 eff in each of the cases. For the case of the quadratic potential with and without the step, we have arrived at results similar to what we have obtained earlier in Chapter 2. Also, as one would expect, we find that the background parameters are better constrained with the inclusion of the additional SDSS data [134]. Moreover, it is obvious from Table 6.2 that the axion monodromy model does not lead to the same extent of improvement in the fit as we had obtained in Chapter 3. This occurs due to the fact that, unlike in the earlier analysis, we have not evaluated the CMB angular power at each multipole, but have worked with the inbuilt effective sampling and interpolation routine in CAMB. However, we should 114
6.4. RESULTS Model Quadratic Quadratic + step Quadratic + sine Axion monodromy Ω b h 2 0.0222 0.0221 0.0216 0.0225 Ω c h 2 0.1162 0.1159 0.1168 0.1154 θ 1.038 1.039 1.036 1.039 τ 0.0824 0.0875 0.0836 0.0856 ln (10 10 A) -0.6545 -0.6406 -0.6448 0.9649 α - 1.61×10 −3 6.35×10 −5 4.4×10 −5 φ 0 /M Pl - 14.664 - - ∆φ/M Pl - 3.22×10 −3 - - ln(β/M Pl ) - - -2.576 -7.61 δ - - 2.208 -1.178 χ 2 eff 7515.57 7507.3 7515.12 7509.56 Table 6.2: The best fit values for the background and the potential parameters for the different models of interest obtained from the MCMC analysis using the WMAP-7 and the SDSS LRG DR7 data. We should mention here that the parameter A denotes λ/M 3 Pl in the case of axion monodromy model and m 2 /M 2 Pl in the rest of the cases. As we have discussed before, the quadratic potential with the step improves the fit to the outliers in the CMB data around the multipoles of l = 22 and 40. Moreover, as we have seen, while the superimposed sinusoidal modulation to the quadratic potential does not provide a better fit to the data when compared to the quadratic potential, the axion monodromy model improves the fit to a good extent. However, note that, the monodromy model does not improve the fit to the data to the same extent that we had discussed in Chapter 3. As we have pointed out in the text, this arises due to the limited sampling and interpolation by CAMB over the multipoles of interest which we have chosen to work with. stress that this does not affect our conclusions since our focus here lies on the maximum change in the formation of halos. Therefore, we are more interested in the allowed regions of the parameter space rather in arriving at the precise best fit point. Also, importantly, as we shall discuss in the following subsection, for violent oscillations in the primordial power spectrum (when one requires computing the CMB angular power spectrum at each multipole explicitly), the percentage change in the number density of halos proves to be negligible in the observable mass bins. In Figure 6.2, we have illustrated the one dimensional likelihood on the parameter φ 0 in the case of the quadratic potential with a step, and it is clear that the location of the step is highly constrained by data. The step affects the number density of halos only over 115
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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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Page 135 and 136: 6.2. FROM THE PRIMORDIAL SPECTRUM T
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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
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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
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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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