= Linear matter perturbation growth equation
{title2=$\ddot\delta+2H\dot\delta-4\pi G\bar\rho_m\delta=0$}
For pressureless sub-Hubble perturbations, combine the <linearized cosmological continuity equation>, <cosmological Euler equation> and gravitational <Poisson equation> with matter as its source. The expansion contributes a $2H$ friction term and matter self-gravity contributes the negative coefficient of $\delta$. The background expansion can include radiation or dark energy; treating their perturbations as additional sources requires a more complete system.
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