Baryon--cold-dark-matter relative density mode
= Baryon--cold-dark-matter relative density mode
{title2=$D=\delta_c-\delta_b$}
After recombination and when pressure is negligible, cold dark matter and baryons feel the same gravitational acceleration. Their density-contrast difference therefore obeys
$$
\ddot D+2H\dot D=0.
$$
During matter domination $D=D_0+D_1a^{-1/2}$, whereas the growing total-matter mode is proportional to $a$, so $\delta_c/\delta_b\to1$.