Structure Formation

Cosmology · Part 5

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Table of Contents

  1. 1.1. Introduction
  2. 2.2. Linear Perturbation Theory
  3. 3.3. The Jeans Instability
  4. 4.4. The Transfer Function
  5. 5.5. The Matter Power Spectrum
  6. 6.6. Nonlinear Gravitational Collapse
  7. 7.7. The Cosmic Web
  8. 8.8. The Press-Schechter Formalism
  9. 9.9. Computational Exercise: Matter Power Spectrum and Growth Factor
  10. 10.10. Summary

Key Equations

$$\delta(\mathbf{x}, t) \equiv \frac{\rho(\mathbf{x}, t) - \bar{\rho}(t)}{\bar{\rho}(t)}$$
$$D(a) = \frac{5\Omega_{m,0}}{2}\,H(a)\int_0^a \frac{da'}{[a' H(a')]^3}$$
$$\boxed{P(k, z) = A\,k^{n_s}\,T^2(k)\,D^2(z)}$$
$$\mathbf{x}(\mathbf{q}, t) = \mathbf{q} + D(t)\,\mathbf{\Psi}(\mathbf{q})$$

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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