Total and relative density modes of two pressureless matter fluids
= Total and relative density modes of two pressureless matter fluids
For constant fractions $f_B,f_D$ in an <Einstein-de Sitter universe>, $S=f_B\Delta_B+f_D\Delta_D$ obeys the usual self-gravitating growth equation, while $D=\Delta_D-\Delta_B$ obeys $\ddot D+4\dot D/(3t)=0$. Thus $S=A t^{2/3}+B t^{-1}$ and $D=C+E t^{-1/3}$. The individual contrasts are $\Delta_B=S-f_DD$ and $\Delta_D=S+f_BD$.