Structure formation in dark energy cosmologies described by PADE parametrization

We study the imprints on the formation of cosmic structures of a particular class of dark energy parametrizations dubbed PADE parametrization. Here we investigate how dark energy can affect the growth of large-scale structures of the universe in the framework of spherical collapse model. The dynamics of the spherical collapse of a dark matter halo depends on the properties of the dark energy model. We show that the properties of spherical collapse scenario are directly affected by the evolution of dark energy. We obtain the main parameters of spherical collapse for two different DE parametrizations in two different approaches: first the homogeneous DE approach, in which dark energy does not exhibit fluctuations on cluster scales and the other, clustered DE scenario in which, dark energy components inside the overdense region collapses similar to dark matter. Using the Sheth-Tormen mass function, we investigate the abundance of virialized haloes in the framework of PADE parametrizations. Specifically, the present analysis shows that the number count of darkmatter haloes depends on the evolution of DE parametrizations and clustering properties of dark energy. Also we show that perturbations in phantom DE components enhance the growth of matter perturbations. This result was obtained in the literature for dark energy parametrizations that are phantom at all redshifts. But we obtained same results for dark energy parametrizations which are in phantom regime and enter in quintessence region at relatively low redshifts. We also show that in parametrizations under study, low-mass haloes were formed before massive haloes.