Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 The Homogeneous and Isotropic Universe
- 2 Perturbation Theory
- 3 Initial Conditions
- 4 CMB Anisotropies
- 5 CMB Polarization and the Total Angular Momentum Approach
- 6 Non-Gaussianities
- 7 Lensing and the CMB
- 8 Observations of Large-Scale Structure
- 9 Cosmological Parameter Estimation
- 10 The Frequency Spectrum of the CMB
- Appendix 1 Fundamental Constants, Units and Relations
- Appendix 2 General Relativity
- Appendix 3 Perturbations
- Appendix 4 Special Functions
- Appendix 5 Special Functions
- Appendix 6 Mixtures
- Appendix 7 Statistical Utensils
- Appendix 8 Approximation for the Tensor Cℓ Spectrum
- Appendix 9 Boltzmann Equation in a Universe with Curvature
- Appendix 10 Perturbations of the Luminosity Distance
- References
- Index
5 - CMB Polarization and the Total Angular Momentum Approach
Published online by Cambridge University Press: 10 December 2020
- Frontmatter
- Dedication
- Contents
- Preface
- 1 The Homogeneous and Isotropic Universe
- 2 Perturbation Theory
- 3 Initial Conditions
- 4 CMB Anisotropies
- 5 CMB Polarization and the Total Angular Momentum Approach
- 6 Non-Gaussianities
- 7 Lensing and the CMB
- 8 Observations of Large-Scale Structure
- 9 Cosmological Parameter Estimation
- 10 The Frequency Spectrum of the CMB
- Appendix 1 Fundamental Constants, Units and Relations
- Appendix 2 General Relativity
- Appendix 3 Perturbations
- Appendix 4 Special Functions
- Appendix 5 Special Functions
- Appendix 6 Mixtures
- Appendix 7 Statistical Utensils
- Appendix 8 Approximation for the Tensor Cℓ Spectrum
- Appendix 9 Boltzmann Equation in a Universe with Curvature
- Appendix 10 Perturbations of the Luminosity Distance
- References
- Index
Summary
We derive the perturbed Boltzmann equation for CMB photons. After a brief introduction to relativistic kinetic theory, we first derive the Liouville equation, i.e. the Boltzmann equation without collision term. We also discuss the connection between the distribution function and the energy{momentum tensor. We then derive the collision term, i.e. the right-hand side of the Boltzmann equation, due to Thomson scattering of photons and electrons. In this first attempt we neglect the polarization dependence of Thomson scattering. This treatment however includes the finite thickness of the last scattering surface and Silk damping. The chapter ends with a list of the full system of perturbation equations for a ΛCDM universe, including massless neutrinos.
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- Information
- The Cosmic Microwave Background , pp. 208 - 243Publisher: Cambridge University PressPrint publication year: 2020