On the graph at the start of class, why is the acceleration curve shaped as if acceleration slowed down, and then speeded up?
This line represents a particular model of dark energy- I believe it is the cosmological constant model, although they don’t specify that in the text. In this model, the dark energy density (energy/volume) is constant in time. At very early times, when the universe has a very high matter density, the effect of gravity wins out over the dark energy, and the expansion decelerates initially. Then, as the universe expands, the effect of gravity decreases as the matter gets less dense. Because dark energy density never gets any smaller, it starts to dominate the behavior of the universe- the effective repulsive force takes over and the expansion accelerates. In this model (which is consistent with the supernova data), right now dark energy has already started to take over. Note that other models of dark energy would show a differently-shaped curve.
