Observational Cosmology - Unit 2 Solutions

3. From Friedmann's equation:
(a) In an empty universe H(t) scales as 1/a(t), so that da/dt is constant (i.e. a constant velocity expansion).
(b) In the flat case (Einstein-de Sitter model), H(t) scales as sqrt(rho). For a matter-dominated universe rho simply scales as a-3, so that H goes as a-3/2 and da/dt scales as a-1/2.