In Barbara Ryden's Intro to Cosmology, she says that, since we can write the energy density of the universe as $\varepsilon(t) = \sum\limits_{w}\varepsilon_w$, where $w$ runs over the possible equation-of-state parameters of different parts of the universe, and also $P = \sum\limits_{w}w\varepsilon_w$ (from the equation-of-state), then the fluid equation $$ \dot{\varepsilon} + 3\frac{\dot{a}}{a}\left(\varepsilon + P\right) = 0 $$ should hold for each component separately, as long as there is no interaction between the different components.
She then concludes that the energy density of matter falls like $a^{-3}$ and of radiation as $a^{-4}$.
In a latter chapter in her book, when she talks about recombination and decoupling, where matter and radiation clearly interact, she also states that the number density of matter falls like $a^{-3}$. But since matter and radiation do interact, then above conclusion that the fluid equation holds for every component separately, fails.
How, then, can she safely say that the energy density of matter, at the epoch of recombination and decoupling, falls like $a^{-3}$?
