Flat constant-equation-of-state scale factor
= Flat constant-equation-of-state scale factor
For an expanding spatially flat universe with constant $w>-1$ and $a(t_0)=1$,
$$
a(t)=\left[1+\frac32(1+w)H_0(t-t_0)\right]^{2/[3(1+w)]}.
$$
It vanishes at the finite past time $t_*=t_0-2/[3(1+w)H_0]$.