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.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 310 / 4 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-310/4/a/solution