 Baryon catch-up approximation after recombination

In a dark-matter-dominated growing mode with a constant relative offset and initially negligible baryon density contrast, ${\Delta }_B/{\Delta }_D=1-R_r/R=1-(1+z)/(1+z_r)$. Replacing this by $1-z/z_r$ requires high redshift. The initial relative velocity and finite baryon self-gravity alter transients, although the relative difference becomes small as the common growing mode increases.