In spatially flat case (k = 0), the solution for the scale factor is a ( t ) = a 0 t 2 3 ( w + 1 ) where a 0 is some integration constant to be fixed by the choice of initial conditions. This family of solutions labelled by w is extremely important for cosmology. For example, w = 0 describes a matter-dominated universe, where the pressure is negligible with respect to the mass density. From the generic solution one easily sees that in a matter-dominated universe the scale factor goes as a ( t ) ∝ ∝ t 2 / 3 matter-dominated Another important example is the case of a radiation-dominated universe, namely when w = ⁠ 1 / 3 ⁠. This leads to a ( t ) ∝ ∝ t 1 / 2 radiation-dominated