PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 1. INTRODUCTION arise in such cases are often written in the following power law form: P S (k) = A S ( k k ∗ ) nS −1 , (1.24a) P T (k) = A T ( k k ∗ ) nT . (1.24b) The quantities A S and A T denote the amplitude of the scalar and tensor spectra, while n S and n T denote the corresponding spectral indices. The quantity k ∗ is the pivot scale at which the amplitudes of the power spectra are quoted. Given the scalar and the tensor spectra, i.e. P S (k) andP T (k), the tensor-to-scalar ratio is defined as r(k) = P T (k) P S (k) . (1.25) It is the scalar amplitude A S , the tensor-to-scalar ratio r, and the scalar and the tensor indices n S and n T that are typically treated as the observables associated with slow roll inflationary models. Upon comparing with the observations, one arrives at constraints on these four quantities which, in turn, indicate how these models perform against the data. The physics involved in the propagation of the perturbations from their primordial origins (say, during inflation) to their corresponding signatures as anisotropies in the CMB is well understood, at least at the linear order in the perturbation theory [6]. In fact, there exist highly developed and accurate numerical codes such as the Cosmological Boltzmann Code CAMB [43, 44] to arrive at the CMB angular power spectra from the primordial scalar and tensor spectra. These codes, when coupled to Cosmological Monte Carlo codes like COSMOMC [45, 46], greatly facilitate the comparison of inflationary models with the observations of the CMB anisotropies as well as other cosmological data sets such as those involving the LSS. The observed anisotropies in the CMB are usually expressed in terms of the CMB angular power spectra and cross-correlations involving the temperature and the E and the B types of polarizations, viz. C TT l , C TE l , C EE l and C BB l . It is often found that perturbation spectra generated by slow roll inflationary models fit the CMB data from the various missions such as WMAP [17, 18, 19], QUaD [10, 11], ACBAR [13] and ACT [15] rather well (for a more detailed discussion on this topic, see, for example, Ref. [47] and references therein). For instance, one finds that the best fit power law scalar spectra corresponds to the scalar amplitude A S ≃ 2.193 × 10 −9 at the pivot scale of 0.05Mpc −1 (a constraint that is often referred to as COBE normalization [48]), and a spectral index of n S ≃ 0.97 (in this context, see Chapter 2). However, it should be emphasized that we are 16
1.2. THE INFLATIONARY PARADIGM yet to detect any tensor perturbations. The tensor spectral index in the theoretical models often proves to be small enough that it is usually set to be zero when comparing with the observations, while the seven-year WMAP data [19] and the ACT data [15] suggest the upper bound on the tensor-to-scalar ratio r to be 0.24 at 95% Confidence Level (CL). Figure 1.3 below contains a plot of the observed TT angular power spectrum arrived at from seven years of WMAP data and the best fit theoretical angular power spectrum corresponding to power law primordial spectra [19]. It is evident from the figure that the theoretical predictions seem to agree well with the observations. Figure 1.3: The theoretical and the observed CMB (TT) angular power spectra have been plotted as a function of the multipoles l. The black dots with the error bars are the binned data points from seven years of WMAP data [19]. The solid red curve is the analytical best fit angular power spectrum corresponding to power law primordial spectra [cf. Eqs. (1.24)] with values of parameters as quoted in the discussion above. The blue band represents cosmic variance [6]. Clearly, the theoretically predicted curve seem to agree with the observations rather well. (Image courtesy: NASA/LAMBDA data products.) 17
Page 1: 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: 1.2. THE INFLATIONARY PARADIGM The
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 and 54: 2.2. METHODOLOGY, DATASETS, AND PRI
Page 55 and 56: 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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4.3. 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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