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
10 - The Frequency Spectrum of the CMB
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
This final chapter discusses spectral distortions of the CMB. We first introduce the relevant collision processes in a universe with photons and non-relativistic electrons: Compton scattering, Bremsstrahlung and double Compton scattering. We derive the corresponding collision terms and Boltzmann equations. For Compton scattering this leads us to the Kompaneets equation for which we present a detailed derivation. We introduce timescales corresponding to these three collision processes and determine at which redshift a given process freezes, i.e., becomes slower than cosmic expansion. We also discuss the generation of a chemical potential in the CMB spectrum by a hypothetical particle decay and by Silk damping of small scale fluctuations. Finally, we study the Sunyaev{Zel’dovich effect of CMB photons which pass through hot cluster gas.
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- The Cosmic Microwave Background , pp. 388 - 415Publisher: Cambridge University PressPrint publication year: 2020