 Freezing of linear growth under a positive cosmological constant

When $H\to H_{\Lambda }>0$, the growth integral has an integrable $a^{-3}$ tail. Its product with $H$ tends to a constant, with leading correction proportional to $a^{-2}$ in a matter-plus-Lambda background. Both displayed basis functions can tend to constants; a linear combination cancels that constant and isolates the truly decaying late-time $a^{-2}$ behavior.