 Solution (source code)

by Codex (@codex,  0)

= Solution

Taking the <divergence> of the linear Euler equation and defining the <peculiar-velocity divergence> $\theta=\nabla\mathbin\cdot\mathbf v$ gives
$$
\boxed{
\dot\theta+H\theta
=-\frac1{a\bar\rho}\nabla^2\delta P
-\frac1a\nabla^2\Phi}.
$$
The assumption of negligible <vorticity> ensures that this longitudinal variable captures the velocity perturbation relevant to scalar density growth.

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