The Origin of the Large-Scale Structure in the Universe: Theoretical and Statistical Aspects

Abstract

We review some theoretical and statistical aspects of the origin of the large-scale structure in the Universe, in view of the two most widely known and accepted scenarios: the inflaton and the curvaton scenarios. Among the theoretical aspects, we point out the impossibility of having a low inflationary energy scale in the simplest curvaton model. A couple of modifications to the simplest setup are explored, corresponding to the implementation of a second (thermal) inflationary period whose end makes the curvaton field `heavy', triggering either its oscillations or immediate decay. Low scale inflation is then possible to attain with H_\ast being as low as 1 TeV. Among the statistical aspects, we study the bispectrum B_ζ(k_1,k_2,k_3) of the primordial curvature perturbation ζwhose normalisation \fnl gives information about the level of non-gaussianity in ζ. In connection with \fnl, several conserved and/or gauge invariant quantities described as the second-order curvature perturbation have been given in the literature. We review each of these quantities showing how to interpret one in terms of the others, and analyze the respective expected \fnl in both the inflaton and the curvaton scenarios as well as in other less known models for the generation of primordial perturbations and/or non-gaussianities. The δN formalism turns out to be a powerful technique to compute \fnl in multi-component slow-roll inflation, as the knowledge of the evolution of some family of unperturbed universes is the only requirement. We present for the first time this formalism and apply it to selected examples.

Latex file, 129 pages, 11 figures. PhD Thesis. Supervisor: David H. Lyth. v3: Minor corrections implemented following examiners' suggestions. Fixed problems with ps and pdf files. PhD awarded

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Cited by in corpus (5)

• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part II: the Trispectrum
• Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation
• Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models
• Study of General Relativity and $f(R)$ Modified Gravity with Cosmological Constant for Einstein and Jordan Frames