Cosmological Euler equation
= Cosmological Euler equation
For pressureless matter in conformal time and Newtonian gauge,
$$
\mathbf v'+\mathcal H\mathbf v+(\mathbf v\mathbin\cdot\nabla)\mathbf v
=-\nabla\phi.
$$
Its linear curl implies that vorticity decays as $a^{-1}$.