A beginner’s guide to the theory of CMB temperature and polarization power spectra in the line-of-sight formalism

Abstract We present here a detailed, self-contained treatment of the mathematical formalism for describing the theory of polarized anisotropy in the cosmic microwave background. This didactic review is aimed at researchers who are new to the field. We first develop the mathematical tools for describing polarized scattering of CMB photons. Then we take the reader through a detailed derivation of the line-of-sight formalism, explaining the calculation of both temperature and polarization power spectra due to the scalar and tensor perturbations in a flat Universe.