Cosmic Inflation
Cosmology · Part 3
309 KB10 sections4 key equationsLaTeX typeset
Table of Contents
- 1.1. Introduction
- 2.2. The Horizon Problem
- 3.3. The Flatness Problem
- 4.4. The Monopole Problem
- 5.5. The Inflationary Solution
- 6.6. Scalar Field Dynamics
- 7.7. The Slow-Roll Approximation
- 8.8. Inflationary Models
- 9.9. Quantum Fluctuations During Inflation
- 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...