Scale factor vs. cosmic time, normalized to Einstein–de Sitter expansion. The thick line shows a_uni vs. t for ﹩\Omega _{m}=0.27﹩, ﹩\Omega _{\Lambda }=0.73﹩, ﹩h=0.71﹩. For this cosmology the Hubble time is ﹩1/ H_{0}=13.77\ \mathrm{Gyr}\,﹩ and the age of the universe is 13.67 Gyr; the latter serves as the boundary of the plot on the right side. For ﹩\Delta _{0}=0.4﹩, the upper dotted line is the Eulerian estimate on what a_box should be: ﹩a_{\mathrm{box}\,}=( 1+\Delta ) ^{-1/ 3}a_{\mathrm{uni}\,}﹩. The lower dotted line is the Lagrangian estimate ﹩a_{\mathrm{box}\,}=( 1-\Delta / 3) a_{\mathrm{uni}\,}﹩. The thin line is a_box vs. t for the perturbed cosmological parameters.