Kolb E.W., Turner M.S. The early universe (AW, 1988).pdf

Inflation and the Theory of Cosmological Perturbations.pdf

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Inflation and the Theory of Cosmological Perturbations.pdf的文章目录

Contents 1 Introduction 2 Basics of the Big-Bang Model 2.1 Friedmann equations  2.2 Some conformalities  2.3 The early, radiation-dominated universe 2.4 The concept of particle horizon . . . . . . . . . . . . . . . . . . . . . . . . . 3 The shortcomings of the Standard Big-Bang Theory 3.1 The Flatness Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Entropy Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The horizon problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The standard inflationary universe 4.1 Inflation and the horizon Problem . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Inflation and the flateness problem . . . . . . . . . . . . . . . . . . . . . . . 4.3 Inflation and the entropy problem . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Inflation and the inflaton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Slow-roll conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 The last stage of inflation and reheating . . . . . . . . . . . . . . . . . . . . 4.7 A brief survey of inflationary models . . . . . . . . . . . . . . . . . . . . . . 4.7.1 Large-field models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.2 Small-field models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.3 Hybrid models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Inflation and the cosmological perturbations 6 Quantum fluctuations of a generic massless scalar field during inflation 6.1 Quantum fluctuations of a generic massless scalar field during a de Sitter stage 6.2 Quantum fluctuations of a generic massive scalar field during a de Sitter stage 6.3 Quantum to classical transition . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 The power spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Quantum fluctuations of a generic scalar field in a quasi de Sitter stage . . . 7 Quantum fluctuations during inflation 7.1 The metric fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Perturbed affine connections and Einstein’s tensor . . . . . . . . . . . . . . . 7.3 Perturbed stress energy-momentum tensor . . . . . . . . . . . . . . . . . . . 7.4 Perturbed Klein-Gordon equation . . . . . . . . . . . . . . . . . . . . . . . . 7.5 The issue of gauge invariance . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 The comoving curvature perturbation . . . . . . . . . . . . . . . . . . . . . . 7.7 The curvature perturbation on spatial slices of uniform energy density . . . . 7.8 Scalar field perturbations in the spatially flat gauge . . . . . . . . . . . . . . 7.9 Adiabatic and isocurvature perturbations . . . . . . . . . . . . . . . . . . . . 7.10 The next steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.11 Computation of the curvature perturbation using the longitudinal gauge . . 7.12 Gauge-invariant computation of the curvature perturbation . . . . . . . . . . 7.13 Gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.14 The consistency relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 The post-inflationary evolution of the cosmological perturbations 8.1 From the inflationary seeds to the matter power spectrum . . . . . . . . . . 8.2 From inflation to large-angle CMB anisotropy . . . . . . . . . . . . . . . . . 9 Conclusions A Evolution of the curvature perturbation on superhorizon scales References