USAAAO — 2025 First Round

Cosmologists consider three possible universes: universes dominated by baryonic matter (i.e. ordinary matter), universes dominated by radiation, and universes dominated by dark energy (realistically, we consider some mix of the above). An equation written by Alexander Friedmann implies that for a matter-dominated universe, the Hubble parameter is proportional to the square root of that universe’s matter density. In a matter-dominated universe, how does the size of the universe evolve with time t?