Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-312/4/c/solution

Figure 1.
Schematic cosmic microwave background temperature power spectrum and source contributions
. The Sachs-Wolfe contribution controls the low-multipole plateau, acoustic physics produces the peaks, the Doppler contribution is phase shifted, and photon diffusion suppresses the spectrum in the high-multipole damping tail.
The conventional vertical variable is in , plotted against the dimensionless angular multipole . The Sachs-Wolfe effect supplies a nearly flat large-angle plateau for . The total spectrum has its first acoustic peak near with of order , followed by further Cosmic microwave background acoustic peaks; the Doppler CMB anisotropy is phase shifted relative to the photon-density oscillation. At , Cosmic microwave background diffusion damping lets photons random-walk across perturbations during recombination and produces the rapidly falling damping tail.

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