 Flat barotropic matter-vacuum solution

For positive constant cosmological constant, zero cosmological spatial curvature and a separate positive-density fluid with constant equation-of-state parameter $w>-1$, set $H_{\Lambda }=\sqrt{\Lambda /3}$ in the time-unit convention. Eliminating the fluid density gives $\dot{H}=-3(1+w)(H^2-H_{\Lambda }^2)/2$. On the expanding Big Bang branch,The origin is the Big Bang. The fluid's early-time power-law expansion approaches exponential vacuum domination at late times.