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Published online by Cambridge University Press: 10 December 2020
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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