====================
Explanation by words
====================
- Expansion time scale = 1/H [where H = \dot{a}/a]
- Free-fall time = 1/sqrt(G \rho_matter)

During the matter-dominated era: The Friedmann equation gives

H^2 = (8\pi G/3)\rho_matter

Thus, 

1/H ~ 1/sqrt(G \rho_matter) ~ Free-fall time

===================================
Explanation by the minimal equation
===================================
During this period, the density fluctuation defined by

(\rho - \rho_mean)/\rho_mean 

is proportional to the scale factor.

From this, and using the Poisson equation, you can derive 

\Phi = constant.

- Derivation -
\Phi is proportional to a^2(\rho - \rho_mean), which is proportional to

\Phi ~ a^2\rho_mean * a

Since \rho_mean ~ 1/a^3,
i.e., \Phi ~ constant.

===============================
Dark energy => Potential decays
===============================
By words:
    
DE makes the Universe expand faster. Faster than the gravity attracts. Namely, the expansion time scale is shorter than the free-fall time. Thus, matter can't cluster anymore, making \Phi decay.

The Friedmann equation is
H^2 = (8\pi G/3)[\rho_matter + \rho_darkenergy] ~ (8\pi G/3)\rho_darkenergy
=> 1/H ~ 1/sqrt(G \rho_darkenergy)

Free-fall time ~ 1/sqrt(G \rho_matter)

During the DE era, \rho_darkenergy > \rho_matter. Thus,

1/H < Free-fall time => Expansion is "too fast"