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.
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