= Barotropic matter-vacuum acceleration transition
{title2=$(1+z_{\rm tr})^{3(1+w)}=2\Omega_{\Lambda0}/[(1+3w)\Omega_{m0}]$}
For a constant-$w$ material fluid and positive vacuum <energy>, the <Friedmann acceleration equation> gives $\ddot a/(aH_0^2)=\Omega_{\Lambda0}-(1+3w)\Omega_{m0}(1+z)^{3(1+w)}/2$. If $w>-1/3$, its zero determines the displayed transition. A past transition additionally requires the right-hand side of the displayed equation to exceed one. The equation does not imply the same transition for a fluid that already has sufficiently negative <pressure>.
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