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In this paper we obtain observational constraints on three dynamical colddark energy models ,include PL , CPL and FSL, with most recent cosmologicaldata and investigate their implication for structure formation, dark energyclustering and abundance of CMB local peaks. From the joint analysis of the CMBtemperature power spectrum from observation of the Planck, SNIa light-curve,baryon acoustic oscillation, $f\sigma_8$ for large scale structure observationsand the Hubble parameter, the PL model has the highest growth of matterdensity, $ \Delta_{m} $, and matter power spectrum, $ P(k) $, compared to$\Lambda$CDM and other models. For the CPL on the other hand, the structureformation is considerably suppressed while the FSL has behavior similar tostandard model of cosmology. Studying the clustering of dark energy, $\Delta_{DE}$, yields positive but small value with maximum of $\Delta_{DE}\simeq10^{-3} $ at early time due to matter behaviour of the PL,while for the CPL and FSL cross $ \Delta_{DE}=0 $ several time whichdemonstrate void of dark energy with $ \Delta_{DE}\simeq-10^{-11} $ in certainperiods of the history of dark energy evolution. Among these three models, thePL model demonstrate that is more compatible with $ f\sigma_{8} $ data. We alsoinvestigated a certain geometrical measure, namely the abundance of localmaxima as a function of threshold for three DDE models and find that the methodis potentially capable to discriminate between the models, especially far frommean threshold. The contribution of PL and CPL for late ISW are significantcompared to cosmological constant and FSL model. The tension in the Hubbleparameters is almost alleviated in the PL model.

Are Cold Dynamical Dark Energy Models Distinguishable in the Light of the Data?