Cosmic Inflation

Cosmology · Part 3

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Table of Contents

  1. 1.1. Introduction
  2. 2.2. The Horizon Problem
  3. 3.3. The Flatness Problem
  4. 4.4. The Monopole Problem
  5. 5.5. The Inflationary Solution
  6. 6.6. Scalar Field Dynamics
  7. 7.7. The Slow-Roll Approximation
  8. 8.8. Inflationary Models
  9. 9.9. Quantum Fluctuations During Inflation
  10. 10.10. The Primordial Power Spectrum

Key Equations

$$d_H(t) = a(t) \int_0^t \frac{c\,dt'}{a(t')}$$
$$\boxed{a(t) = a_i \exp\!\left(\int_{t_i}^{t} H(t')\,dt'\right) \approx a_i\,e^{H(t - t_i)}}$$
$$\ddot a > 0 \quad \Leftrightarrow \quad \rho + 3p/c^2 < 0 \quad \Leftrightarrow \quad \dot\varphi^2 < V(\varphi)$$
$$\boxed{\mathcal{P}_\mathcal{R}(k) = \left.\frac{1}{2\epsilon}\,\frac{H^2}{(2\pi)^2 M_P^2}\right|_{k = aH} = \left.\frac{1}{24\pi^2}\,\frac{V}{M_P^4\,\epsilon}\right|_{k=aH}}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Cosmology course on CoursesHub.World. Study the origin, structure, and evolution of the universe. Covers the expanding universe, thermal history, cosmic inflation, CMB physics, structure formation, dark matter, dark energy, and observatio...

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