Spherical collapse in a dark energy model with reconstructed effective equation of state

The present work deals with the study of spherical collapse of matter density contrast in a latetime cosmological model with a reconstructed effective equation of state. The linear and nonlinear evolution of matter density contrast are studied. The variation of the critical density at collapse of the spherical overdense region along redshift are also investigate. Further the number count of collapsed object or the dark matter halos, equivalent to the number count of galaxy clusters, are also studied. Two different halo mass function formulations, namely the Press-Schechter mass function and the Sheth-Tormen mass function, are adopetd to study the cluster number count along the redshift. Similar analysis is also carried out for wCDM dark energy model to have a direct comparison with the reconstructed effective equation of state model. These two models are highly degenerate at the background and linear level of matter perturbation. But the nonlinear evolution of matter overdensity breaks the degeneracy. The reconstructed effective equation of state model shows a substantial suppression in the cluster number count compared to wCDM for redshift z > 0.5, and for z < 0.5, the number count is slightly higher than that of wCDM.