 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.