Einstein-de Sitter density-growth modes ($\delta =C_{+}{t}^{2/3}+C_{-}{t}^{-1}$)

For pressureless linear cosmological density perturbations in an Einstein-de Sitter universe, $H=2/(3t)$ and $4\pi G{\bar{\rho }}_m=2/(3t^2)$. The growth equation is an Euler differential equation whose indicial equation is $(p-2/3)(p+1)=0$. Hence the independent modes are ${\delta }_{+}\propto t^{2/3}\propto a$ and ${\delta }_{-}\propto t^{-1}\propto a^{-3/2}$. The first is the growing linear growth factor, while the second is a decaying transient.