PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

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CHAPTER 7. IMPRINTS OF PRIMORDIAL NON-GAUSSIANITY IN THE LY-ALPHA FOREST as we had pointed out in Section 1.7, we shall explicitly display the velocity of light c in this chapter for certain convenience. In our analysis below, we shall assume that the parameter f NL is scale independent, which, as should be evident from our discussion in Chapter 4, is a reasonable prediction for most inflationary models where non-Gaussianity is generated on super-Hubble scales. The value off NL obtained from slow roll inflation turns out to be very smallO(10 −2 ) [49]. This implies that any detection of large f NL shall rule out all canonical, single field, slow roll, inflationary models. However, as we have mentioned, the mean value off NL (26±140 in the equilateral and 32±21 in the local limit, at1-σ confidence level) obtained from the WMAP data [19] seems to indicate large non-Gaussianity. Although the low Signal to Noise Ratio (SNR) in these results indicate that we are yet to detect the primordial non- Gaussianity, it is expected that data from Planck [20] shall lead to much tighter constraints onf NL and the error is expected to come down to∆f NL ≃ ±5 in the local limit. Other than the CMB observations, a measurement of the bi-spectrum or the three point correlation function of the galaxy distribution is a standard alternative method to constrain primordial non-Gaussianity [136]. These probes however only provide weak bounds on the non-Gaussianity parameter as compared to the CMB observations, with SDSS, for example, being able to measure |f NL | of the order of10 3 or 10 4 . In the post reionization epoch, small fluctuations of the neutral hydrogen (HI) density field in a predominantly ionized IGM leads to a series of distinct absorption features, the so-called Ly-α forest in the spectra of background quasars [66]. The Ly-α forest is a well established and powerful probe of cosmology [137, 138]. Traditional Ly-α studies have considered the power spectrum or bi-spectrum of the one dimensional transmitted flux field corresponding to the quasar line of sight [138]. This approach is reasonable when the angular density of quasars on the sky is low. The new generation of quasar surveys (the ongoing BOSS [67] and the future BigBOSS [68]) however promise to achieve a very high quasar density and cover large fractions of the sky. This has led to the possibility of measuring the 3D Ly-α power spectrum along multiple lines of sight [139]. It is worth noting here that the first hydro simulation of the Ly-α forest involving non-Gaussian scenarios has been carried out recently [140]. In this chapter, we shall investigate the possibility of constraining the non-Gaussianity parameterf NL using the 3D Ly-α forest bi-spectrum. Similar to the power spectrum studies, the Ly-α flux distribution is assumed to be a biased tracer of the underlying matter field sampled along discrete sight lines. We shall explore the range of observational parameters for the constraints on f NL from the 3D analysis to be competitive with the CMB 124
7.1. FORMALISM and the LSS studies. 7.1 Formalism The post reionization matter overdensity field ∆(x) in Fourier space (∆ k ) can be related to the primordial gravitational potential (Φ P ) on sub-Hubble scales as follows: The function M(k,z) is given by [cf. Eq. (1.30)] ∆ k (z) = M(k,z)Φ P k . (7.2) M(k,z) = − 3 5 k 2 T(k) Ω m H 2 0 D + (z), (7.3) where, as we had discussed, T(k) denotes the matter transfer function, while D + (z) represents the growth factor associated with the density fluctuations. In our analysis below, we shall make use of the conventional Bardeen-Bond-Kaiser-Szalay (BBKS) transfer function [141] and the cosmological parameters obtained from an MCMC analysis of the WMAP-7 data [85]. Actually, to obtain a more accurate result, a transfer function including the baryonic acoustic oscillations should be made use of. But, since our main motivation here is to arrive at bounds on the bi-spectrum and not to calculate exact numbers, the approximate BBKS transfer function proves to be sufficient. The power spectrum of the density field is defined as 〈∆ k ∆ k ′〉 = P(k)δ (3) (k+k ′ ). (7.4) Clearly, the linear power spectrum of the density field is given byP(k) = M 2 (k,z)P P Φ (k), wherePΦ P denotes the primordial power spectrum of the gravitational potential such that PΦ P = P Φ G + O(f 2 ). [Note that the matter power spectrum P(k) above is the same as NL the quantity P M (k) defined in Eq. (1.30). We shall drop the subscript in this chapter for convenience.] The power spectrum P ΦG of the Gaussian field Φ G shall be assumed to be featureless and scale invariant. Following the power spectrum which is the two point correlator of the density field, the n point correlators can be defined as 〈∆ k1 ∆ k1 ...∆ kn 〉 = and, using the definition above, we define the bi-spectrum as n∏ M(k i )〈Φ P k 1 Φ P k 2 ...Φ P k n 〉 (7.5) i=1 〈∆ k1 ∆ k2 ∆ k3 〉 = B(k 1 ,k 2 ,k 3 )δ (3) (k 1 +k 2 +k 3 ). (7.6) 125
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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 97 and 98: 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
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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 and 144: 6.4. RESULTS 30 4 20 Change in R Ch
Page 145 and 146: 6.5. DISCUSSION wherein one works w
Page 147: Chapter 7 Imprints of primordial no
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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