= Cosmological fate from local expansion data
{title2=$\rho_{m0}=(H_0^2-A_0)/(4\pi G),\quad\Lambda c^2=H_0^2+2A_0$}
For a spatially flat universe consisting only of dust and constant <cosmological constant>, $A_0=\ddot a_0/a_0$ and $H_0$ determine the two model parameters through the <Friedmann equations>. Predicting the future also assumes those matter laws persist. Local derivatives alone do not determine arbitrary future stress evolution: $a_+(t)=1+t+t^2/2$ and $a_-(t)=1+t+t^2/2-t^3$ agree through second derivative at zero, but the first expands forever and the second recollapses.
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