Constant-equation-of-state density scaling

For constant $w\ne -1$, the cosmological continuity equation integrates towhen $a=1$ at the reference time and ${\rho }_0$ is the reference density.

For an expanding spatially flat universe with constant $w>-1$ and $a(t_0)=1$,It vanishes at the finite past time $t_{\ast }=t_0-2/[3(1+w)H_0]$.