  This conference proceedings paper provides a short summary of the constraints
presented by Menci et al. (2020) and Menci et al. (2022) to dynamical dark
energy models. Dynamical dark energy (DDE) models have been proposed to address
several observational tensions arising within the standard $\Lambda$ cold dark
matter ($\Lambda$CDM) scenario. Different DDE models, parameterized by
different combinations of the local value of the equation-of-state parameter
$w_0$ and its time derivative $w_a$, predict different maximal abundance of
massive galaxies in the early Universe. We use the observed abundance of
massive galaxies already in place at z>=4.5 to constrain DDE models. To this
aim, we consider four independent probes: (i) the observed stellar mass
function at z~6 from the CANDELS survey; (ii) the estimated volume density of
massive haloes derived from the observation of massive, star-forming galaxies
detected in the submillimeter range at z~5; (iii) the rareness of the most
massive system detected at z~7 by the SPT survey; (iv) the abundance of massive
(M>10^10.5 Msun) galaxies at z~10 as inferred from early JWST observations. Our
probes exclude a major fraction of the DDE parameter space that is allowed by
other existing probes. In particular, early JWST results, if confirmed, are in
tension with the standard $\Lambda$CDM scenario at a 2$\sigma$ confidence
level.
