PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 2. GENERATION OF LOCALIZED FEATURES and the perturbations using a fast and accurate Fortran 90 code that treats the e-folds N as the independent variable. The perturbations are evolved using the governing equations (1.16) and (1.18) from the Bunch-Davies initial conditions (1.23) imposed when the modes are well inside the Hubble radius. The power spectra [cf. Eqs. (1.21) and (1.22)] are evaluated when the modes are sufficiently outside the Hubble radius, when the amplitude of the perturbations have reached their asymptotic values [81, 82]. We should add here that, while the speed of propagation of the curvature perturbations induced by the canonical scalar field is a constant (and, equal to unity), it changes with time in the case of the tachyon models [79, 83]. This point needs to be carefully taken into account, while imposing the initial conditions on the modes as well as when evolving them from the sub-Hubble to the super-Hubble scales. In order to arrive at the constraints on the various background cosmological parameters and the parameters describing the inflaton potential, we perform a Markov Chain Monte Carlo (MCMC) sampling of the parameter space. To do so, we make use of the publicly available COSMOMC package [45, 46], which in turn uses the CMB anisotropy code CAMB [44, 43] to generate the CMB angular power spectra from the primordial scalar and tensor spectra. We evaluate the scalar and the tensor spectra for all the modes that are required by CAMB to arrive at the CMB angular power spectra. For our analysis, we consider the following CMB datasets: the WMAP five-year [18] and seven-year data [19], the QUaD June 2009 data [11], and the the ACBAR 2008 data [13]. We have separately compared the models with the WMAP five-year and seven-year data. We have also compared the models with the WMAP five-year data along with the QUaD data, and with the QUaD as well as the ACBAR data. We have used the October 2009 version of COSMOMC (and CAMB) while comparing with the WMAP five-year and the QUaD and the ACBAR datasets. When comparing with the WMAP seven-year data, we have made use of a more recent version (i.e. the January 2010 version) of COSMOMC and CAMB. In our analysis, we take gravitational lensing into account. Note that, to generate highly accurate lensed CMB spectra, CAMB requires l max scalar ≃ (l max +500), where l max is, say, the largest multipole moment for which the data is available. The WMAP data is available up to l ≃ 1200, the QUaD data goes up to l ≃ 2000, while the ACBAR data is available up to l ≃ 2700. So, we set l max scalar = 2500 when dealing with the WMAP and the QUaD datasets and, when we include the ACBAR data, we set l max scalar = 3300. Since the datasets involve rather large multipole moments (say, l 1000), we also take into account the Sunyaev-Zeldovich effect, and marginalize over the A SZ parameter. For the power law case, we set the pivot scale to be k ∗ = 0.05Mpc −1 [cf. Eq. (1.24)]. We 30
2.2. METHODOLOGY, DATASETS, AND PRIORS have made use of the publicly available WMAP likelihood code from the LAMBDA website [84] to determine the performance of the models against the data. We have have set the Gelman and Rubin parameter |R − 1| to be 0.03 for convergence. Lastly, we should add that we have used the Gibbs option (for the CMBTT spectrum at the low multipoles) in the WMAP likelihood code to evaluate the least square parameterχ 2 eff . As we had mentioned earlier, we incorporate the tensor perturbations in our analysis. Recall that, in the power law case, when the consistency condition between the tensorto-scalar ratior and the tensor spectral indexn T is not imposed, both these quantities are required to describe the tensor power spectrum. They need to be specified along with the scalar amplitude A S and the corresponding spectral index n S , in order to completely determine the primordial spectra. We should emphasize that, in the other inflationary models, once the parameters that govern the potential have been specified, no further parameters are required to describe the tensor power spectrum. The potential parameters determine the amplitude and shape of both the scalar and the tensor spectra. We shall assume the background to be a spatially flat, ΛCDM model described by the four standard parameters, viz.Ω b h 2 andΩ c h 2 , which represent the baryon and CDM densities (with h being related to the Hubble parameter), respectively, the ratio of the sound horizon to the angular diameter distance at decoupling θ, and τ which denotes the optical depth to reionization. We shall work with the following priors on these parameters: 0.005 ≤ Ω b h 2 ≤ 0.1, 0.01 ≤ Ω c h 2 ≤ 0.99, 0.5 ≤ θ ≤ 10.0 and 0.01 ≤ τ ≤ 0.8. We should add that we keep the same priors on the background parameters for all the models and datasets that we shall consider in our analysis. In Table 2.1, we have listed the priors that we choose on the different parameters which describe the various inflationary models that we consider. 31
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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
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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 and 50: Chapter 2 Generation of localized f
Page 51 and 52: 2.1. THE INFLATIONARY MODELS OF INT
Page 53: 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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4.4. 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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