= Hubble parameter as a solution of the dust growth equation
{c}
{title2=$D_-(t)\propto H(t)$}
For dust, curvature and a constant <cosmological constant>, write $H^2=Aa^{-3}+Ba^{-2}+C$. Then $\dot H=-3Aa^{-3}/2-Ba^{-2}$ and $\ddot H=H(9Aa^{-3}/2+2Ba^{-2})$, which imply $\ddot H+2H\dot H-3Aa^{-3}H/2=0$. Thus $H$ is a solution of the pressureless <linear matter perturbation growth equation>. In an <Einstein-de Sitter universe>, $H\propto t^{-1}$ is the decaying mode and the independent growing mode is $t^{2/3}$. Additional dynamical components need not preserve this identity.
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