Einstein-de Sitter metric growing mode ($h=A{\tau }^2+B{\tau }^{-3}$)

For the scalar metric variable satisfying $\ddot{h}+(\dot{R}/R)\dot{h}=4\pi G{\bar{\rho }}_m{R}^{2}h$, the Einstein-de Sitter universe has $\dot{R}/R=2/\tau$ and $4\pi G{\bar{\rho }}_m{R}^2=6/{\tau }^2$. The indicial equation is $p(p-1)+2p=6$, giving exponents $2$ and $-3$. Growth of this metric variable is not growth of every gauge-invariant potential; the growing dust density contrast is compatible with constant scalar gravitational potentials.