Spherical collapse and the holographic dark energy model

In this work we investigate the spherical collapse model in flat FRW universe containing dark energy component. We consider the Holographic Dark Energy (HDE) model as a dynamical dark energy scenario with slowly time varying EoS parameter $w_{\Lambda}$ in order to calculate the effect of dark energy on the scenario of structure formation in the universe. We first calculate the evolution of density perturbation in linear regime for both phantom and quintessence behavior of HDE model and compare the results with standard CDM and $\Lambda$ CDM models. Then we calculate the evolution of two parameters characterizing the spherical collapse model i.e., linear density threshold $\delta_c$ and virial over-density $\Delta_{vir}$ for phantom and quintessence HDE models. It is shown that the growth factor and $\delta_c$ fall behind in $\Lambda$CDM universe. We also show that $\Delta_{vir}$ is largest in quintessence HDE model, intermediate in phantom HDE compare to $\Lambda$CDM model. Hence the growth of structures start earlier in quintessence and phantom HDE models than $\Lambda$CDM and more concentrated objects can be produced in these models.