Abstract
The observed CMB anisotropies that we calculate in this chapter are a combination of three contributions: the monopole, which includes intrinsic photon temperature perturbation and gravitational redshift. This contribution shows acoustic oscillations, whose behavior is to first order described by the semi-analytic tight-coupling solution. The dipole, or Doppler-shift contribution shows the same acoustic oscillations but is out of phase. Finally, the integrated Sachs–Wolfe contributions is due to the time evolution of gravitational potentials around recombination and at late times. This contribution has a smooth scale dependence. These results allow us to understand how various cosmological parameters impact the observed power spectrum of the CMB, how the CMB constrains them, and what degeneracies persist.
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