 Solution

Yes. A perturbation of amplitude $A$ at CMB decoupling must grow by at least $A^{-1}$ before becoming nonlinear. During matter domination ${\delta }_m\propto a$, but once ${\rho }_{\Lambda }$ dominates, the suppression of matter growth by smooth accelerated expansion makes the growth approach a finite limit. Increasing ${\rho }_{\Lambda }$ moves this freeze-out to an earlier scale factor and eventually prevents ${\delta }_m$ from reaching unity.

For an order-of-magnitude bound, matter growth would reach unity atRequiring matter still to dominate then gives the galaxy-formation bound on the cosmological constantThe exact upper limit follows by imposing $A{D}_{+}(\infty )/D_{+}(a_{\mathrm{dec}})\gtrsim 1$ with the integral growth factor and an appropriate nonlinear-collapse threshold.