Baryon--cold-dark-matter relative density mode ($D={\delta }_c-{\delta }_b$)

After recombination and when pressure is negligible, cold dark matter and baryons feel the same gravitational acceleration. Their density-contrast difference therefore obeysDuring matter domination $D=D_0+D_1{a}^{-1/2}$, whereas the growing total-matter mode is proportional to $a$, so ${\delta }_c/{\delta }_b\to 1$.