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.
