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We study the imprints on the formation of cosmic structures of a particularclass of dark energy parameterizations dubbed PADE parameterization. Here weinvestigate how dark energy can affect the growth of large scale structures ofthe universe in framework of spherical collapse model. The dynamics of thespherical collapse of a dark matter halo depends on the properties of the darkenergy model. We show that the properties of spherical collapse scenario aredirectly affected by the evolution of dark energy. We obtain the mainparameters of spherical collapse for two different DE parameterizations in twodifferent approaches: first the homogeneous DE approach, in which dark energydoes not exhibit fluctuations on cluster scales and the other, clustered DEscenario in which, dark energy components inside the overdense region collapsessimilar to dark matter. Using the Sheth-Tormen mass function, we investigatethe abundance of virialized halos in the framework of PADE parameterizations.Specifically, the present analysis shows that the number count of dark matterhalos depends on the evolution of DE parameterizations and clusteringproperties of dark energy. Also we show that perturbations in phantom DEcomponents enhance the growth of matter perturbations. This result wereobtained in the literature for dark energy parameterizations that are phantomat all redshifts. But we obtained same results for dark energyparameterizations which are in phantom regime and enter in quintessence regionat relatively low redshifts. We also show that in parameterizations understudy, low mass halos were formed before massive halos.

Structure formation in dark energy cosmologies described by PADE parameterization