Spherical collapse in reconstructed dark energy models

The present work deals with the spherical collapse of matter overdensity for two reconstructed dark energy models. One of the models is reconstructed from parametrization of effective or total equation of state of energy components in the universe ($w_{eff}$ model) and the other model is the constant dark energy equation of state model, namely the $w$CDM model. The linear and nonlinear evolution of matter density contrast are studied for the present models. It is observed that the linear and even the nonlinear evolutions of density contract are almost indistinguishable in these two models. The critical density contrast at collapse as a function of redshift is also studied. The nature of critical density contrast is also found to be degenerate in the present models. Further the number count of collapsed objects or dark matter halos along redshift are also studied. Two different halo mass functions, namely the Press-Schechter mass function and the Sheth-Tormen mass function, are adopted in this context. It is observed that for both the mass functions the $w_{eff}$ model has slightly higher number of halos at very low redshift ($z<0.5$) and at higher redshift the $w$CDM model has higher number of dark matter halos. On the other hand, it is observed that the Press-Schechter mass function produces slightly higher number of dark matter halos at low redshift compared to Sheth-Torman mass function and the number of halos is higher for Sheth-Torman mass function at redshift $z>0.9$ for both the dark energy models. The results clearly show that these two highly degenerate dark energy models are distinguishable in the study of spherical collapse and galaxy cluster number counts.