The https://www-thphys.physics.ox.ac.uk/people/AndreiStarinets/TUTORIALS_NOTES_GR/gr-cosmology-exam-paper-2011-solutions.pdf#page=22[official notes, PDF pp. 22–23, handwritten pp. 15–16] give both density scalings, integrate the radiation- and matter-dominated <Friedmann equations>, normalize the late solution today, and match the two approximations at equality.

Solution

Past exam of the general relativity and cosmology and condensed matter physics paper of Part B of the physics course of the University of Oxford / 2011 / Section V / 4 / Unlettered 1 / Solution

 Solution (source code)