Spherical “top-hat” collapse in general-Chaplygin-gas-dominated universes

We expand previous works on the spherical “top-hat” collapse framework in generalized-Chaplygin-gas-dominated universes. Here we allow the collapse in all energetic components within the system. We analyze the nonlinear stages of collapse for various choices of parameter $\alpha$ of the generalized-Chaplygin-gas model introducing an exact formulation for the so-called effective sound speed, $c_{\mathrm{eff}}^2$. We show that, within the spherical top-hat collapse framework, the growth of the structure becomes faster with increasing values of $\alpha$.

Figure 1

Growth of perturbations for the SC-TH in gCg-dominated universes. Top: ${\delta }_b$ vs $z$. Bottom: ${\delta }_{gcg}$ vs $z$.

Figure 2

gCg’s $w_c$ and $w$ evolution with redshift for all the models presented in Table . Higher values of $\alpha$ result in values of $w_c$ closer to zero throughout the collapse and in a later transition from DM- to DE-dominated stages of the gCg universes.

Figure 3

gCg’s $c_{\mathrm{eff}}^2$ and $c_s^2$ evolution with redshift for all the models presented in Table . Note that, while the value of $c_s^2$ increases with the value $\alpha$, the value of $c_{\mathrm{eff}}^2$ will have much more complex dependence.

Figure 4

Collapsed region expansion rate, $h$, evolution with $z$. Note that the redshift of turnaround $z_{ta}$ ($h\simeq 0$) is different for each model and for higher values of $\alpha$ it happens at higher redshifts.

Figure 5

Dependence of $z_{ta}$ on the parameters $\alpha$ and $\overline{C}$. Top: $z_{ta}$ vs $\alpha$ for different values of $\overline{C}$. Bottom: $z_{ta}$ vs $\overline{C}$ for different values of $\alpha$.