Zero-initial-baryon-velocity catch-up transient
= Zero-initial-baryon-velocity catch-up transient
In the dark-matter-dominated limit, imposing both $\Delta_B(t_r)=0$ and $\dot\Delta_B(t_r)=0$ requires a relative decaying mode. With $x=R/R_r$, the ratio becomes $1-3x^{-1}+2x^{-3/2}$. It has a different early-time approach from the constant-offset branch and the same late-time common growth.