= Solution
The https://www-thphys.physics.ox.ac.uk/people/AndreiStarinets/TUTORIALS_NOTES_GR/gr-cosmology-exam-paper-2011-solutions.pdf#page=24[official notes, PDF pp. 24–27, handwritten pp. 17–20] obtain the <photon number density> by integrating the <Planck distribution>, explain the temperature and dilution scalings, and compare the interaction time with the expansion time for <thermal equilibrium>. They also correct the missing cube and factor-of-two error in the paper's printed <photon number density>.
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