The https://www-thphys.physics.ox.ac.uk/people/AndreiStarinets/TUTORIALS_NOTES_GR/gr-cosmology-exam-paper-2011-solutions.pdf#page=17[official notes, PDF pp. 17–18, handwritten pp. 10–11] give the <matter density>, curvature and <cosmological constant> scalings and the requested logarithmic sketch. For the closed model the curvature contribution to the <Friedmann equations> is negative; the sketched curvature magnitude must be read with that sign restored.

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 / 3 / Unlettered 1 / Solution

 Solution (source code)