  We compare the maximal abundance of massive systems predicted in different
dynamical dark energy (DDE) models at high redshifts z = 4-7 with the measured
abundance of the most massive galaxies observed to be already in place at such
redshifts. The aim is to derive constraints for the evolution of the dark
energy equation of state parameter w which are complementary to existing
probes. We adopt the standard parametrization for the DDE evolution in terms of
the local value w_0 and of the look-back time derivative w_a of the equation of
state. We derive constraints on combinations (w_0, w_a) in the different DDE
models by using three different, independent probes: (i) the observed stellar
mass function of massive objects at z = 6 derived from the CANDELS survey; (ii)
the estimated volume density of massive halos derived from the observation of
massive, star-forming galaxies detected in the submillimeter range at z = 4;
(iii) The rareness of he most massive system (estimated gas mass exceeding 3
10^11 M_sun) observed to be in place at z = 7, a far-infrared-luminous object
recently detected in the South Pole Telescope (SPT) survey. Finally, we show
that the combination of our results from the three above probes excludes a
sizable fraction of the DDE parameter space w_a > -3/4 - (w_0 + 3/2) presently
allowed (or even favored) by existing probes.
