For matter-dominated universes, where Ω 0,M ≫ Ω 0,R and Ω 0, Λ, as well as Ω 0,M ≈ 1 : t H 0 = ∫ ∫ 0 a d a ′ Ω Ω 0 , M a ′ − − 1 t H 0 Ω Ω 0 , M = ( 2 3 a ′ 3 / 2 ) | 0 a ( 3 2 t H 0 Ω Ω 0 , M ) 2 / 3 = a ( t ) which recovers the aforementioned a ∝ t