Growing-mode velocity potential in matter domination
= Growing-mode velocity potential in matter domination
{title2=$v=-\eta\phi/3\propto a^{1/2}$}
During <matter domination> in a flat universe, the growing <comoving-gauge density contrast> is proportional to $a\propto\eta^2$. Its Newtonian potential is constant by the Poisson constraint. The momentum constraint gives $v=-2\phi/(3\mathcal H)=-\eta\phi/3$. Thus the peculiar velocity potential grows as $a^{1/2}$ in the convention where the peculiar velocity is $\nabla v$.