Spherical collapse model in agegraphic dark energy cosmologies

Under the commonly used spherical collapse model, we study how dark energy affects the growth of large scale structures of the Universe in the context of agegraphic dark energy models. The dynamics of the spherical collapse of dark matter halos in nonlinear regimes is determined by the properties of the dark energy model. We show that the main parameters of the spherical collapse model are directly affected by the evolution of dark energy in the agegraphic dark energy models. We compute the spherical collapse quantities for different values of agegraphic model parameter $\alpha$ in two different scenarios: first, when dark energy does not exhibit fluctuations on cluster scales, and second, when dark energy inside the overdense region collapses similar to dark matter. Using the Sheth-Tormen and Reed mass functions, we investigate the abundance of dark matter halos in the framework of agegraphic dark energy cosmologies. The model parameter $\alpha$ is a crucial parameter in order to count the abundance of dark matter halos. Specifically, the present analysis suggests that the agegraphic dark energy model with a bigger (smaller) value of $\alpha$ predicts less (more) virialized halos with respect to that of $\mathrm{\Lambda }\mathrm{CDM}$ cosmology. We also show that in agegraphic dark energy models, the number of halos strongly depends on clustered or uniformed distributions of dark energy.

Figure 1

The redshift evolution of the equation of state parameter of NADE $w_{\mathrm{d}}(z)$ (top panel), ratio of dimensionless Hubble parameter of NADE model to the $\mathrm{\Lambda }\mathrm{CDM}$ model (middle panel), and ratio of DE density parameter ${\mathrm{\Omega }}_{\mathrm{d}}(z)$ to ${\mathrm{\Omega }}_{\mathrm{\Lambda }}(z)$ (bottom panel) for different values of model parameter $\alpha$ considered in this work. The red dotted, blue dashed, and green dot-dashed curves correspond to NADE models with $\alpha =2$, $\alpha =3$, and $\alpha =4$, respectively. The reference $\mathrm{\Lambda }\mathrm{CDM}$ model is shown by the black solid line.

Figure 2

The evolution of growth factor (top panel) and ISW (bottom panel) as a function of redshift $z$ for different values of model parameter $\alpha$ considered in this work. The red dotted, blue dashed, and green dot-dashed curves correspond to NADE models with $\alpha =2$, $\alpha =3$, and $\alpha =4$, respectively. Thick and thin curves represent clustered and homogeneous NADE, respectively. The reference $\mathrm{\Lambda }\mathrm{CDM}$ (EdS) model is shown by the thick (thin) solid black line.

Figure 3

Linear overdensity parameter ${\delta }_{\mathrm{c}}$ as a function of $z_{\mathrm{c}}$ (top panel) and ratio of linear overdensity parameter of NADE to that of the $\mathrm{\Lambda }\mathrm{CDM}$ as a function of $z_{\mathrm{c}}$ (bottom panel), for different values of model parameter $\alpha$ considered in this work. Line styles and colors are the same as in Fig. 2.

Figure 4

Redshift evolution of virial overdensity parameter ${\mathrm{\Delta }}_{\mathrm{vir}}$ (top panel) and turnaround overdensity $\zeta$ (bottom panel) for different values of model parameter $\alpha$ considered in this work. Line styles and colors are the same as in Fig. 2.

Figure 5

The redshift evolution of the ratio of DE to dark matter mass $\epsilon (z)$ calculated according to Eq. (29) for different values of NADE model parameter $\alpha$ considered in this work. The red dotted, blue dashed, and green dot-dashed curves correspond to clustered NADE model with $\alpha =2$, $\alpha =3$, and $\alpha =4$, respectively.

Figure 6

Ratio of the number density of cluster-size halos above a given mass $M$ for different NADE models to the concordance $\mathrm{\Lambda }\mathrm{CDM}$ cosmology at $z=0$ (first row panels), $z=0.5$ (second row panels), $z=1.0$ (third row panels), and $z=2.0$ (fourth row panels). Line styles and colors are same as in Fig. 2.

Figure 7

Redshift evolution of the number density of cluster-size halos normalized to that of the $\mathrm{\Lambda }\mathrm{CDM}$ model calculated for different mass scales: $M>{10}^{13}{M}_{\mathrm{sun}}{h}^{-1}$, $M>{10}^{14}{M}_{\mathrm{sun}}{h}^{-1}$, and $M>{10}^{15}{M}_{\mathrm{sun}}{h}^{-1}$ in NADE and $\mathrm{\Lambda }\mathrm{CDM}$ models. Line styles and colors for ST and Reed mass functions are shown in the legends.