Cosmological perturbations in a mimetic matter model

We investigate the cosmological evolution of a mimetic matter model with arbitrary scalar potential. The cosmological reconstruction—which is the method for constructing a model for an arbitrary evolution of the scale factor—is explicitly performed for different choices of potential. The cases where the mimetic matter model shows the evolution as cold dark matter (CDM), the $w\mathrm{CDM}$ model, dark matter and dark energy with a dynamical $Om(z)$ [where $Om(z)\equiv [(H(z)/H_0{)}^2-1]/[(1+z{)}^3-1]$], and phantom dark energy with a phantom-nonphantom crossing are presented in detail. The cosmological perturbations for such evolutions are studied in the mimetic matter model. For instance, the evolution behavior of the matter density contrast (which is different than the usual one, i.e., $\ddot{\delta }+2H\dot{\delta }-{\kappa }^2\rho \delta /2=0$) is investigated. The possibility of a peculiar evolution of $\delta$ in the model under consideration is shown. Special attention is paid to the behavior of the matter density contrast near the future singularity, where the decay of perturbations may occur much earlier than the singularity.

Figure 1

Comparison of the time dependence of the scale factor between the $w\mathrm{CDM}$ model and Eq. (2.20). The thick solid line, solid line, dashed line, and dotted line represent Eq. (2.20) with $w=-0.7$, Eq. (2.20) with $w=-0.9$, the $w\mathrm{CDM}$ model with $w=-0.7$, and the $w\mathrm{CDM}$ model with $w=-0.9$, respectively. $H_0=74\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$, ${\mathrm{\Omega }}_{m0}=0.3$, and ${\mathrm{\Omega }}_{w0}=0.7$ are assumed.

Figure 2

Redshift dependence of the growth-rate function $f(z)$ in mimetic $w\mathrm{CDM}$. The dot-dashed line, solid line, and dashed line represent $f(z)$ in the cases $w=-1.2$, $w=-1$, and $w=-0.8$, respectively. The values ${\mathrm{\Omega }}_{w0}=0.73$, ${\mathrm{\Omega }}_{dm0}=0.23$, and ${\mathrm{\Omega }}_{b0}=0.04$ are assumed in the figure. The initial conditions are $f^{\prime \prime }(100)=f^{\prime }(100)=0$ and $f(100)=1$.

Figure 3

Difference between the mimetic $w\mathrm{CDM}$ and $w\mathrm{CDM}$ models in the growth-rate function $f(z)$ when $w=-0.8$.

Figure 4

Difference between the mimetic $w\mathrm{CDM}$ and $w\mathrm{CDM}$ models in the growth-rate function $f(z)$ when $w=-1.2$.

Figure 5

The growth-rate function $f(z)$ when the evolution of the background space-time is described by Eq. (2.24). The solid, dashed, and dot-dashed curves represent $f(z)$ in this model, $f(z)$ in the $\mathrm{\Lambda }\mathrm{CDM}$ model with ${\mathrm{\Omega }}_{m0}{h}^2=0.142$, and $f(z)$ in the $\mathrm{\Lambda }\mathrm{CDM}$ model with ${\mathrm{\Omega }}_{m0}{h}^2=0.122$, respectively. The initial conditions are $f^{\prime \prime }(100)=f^{\prime }(100)=0$ and $f(100)=1$.

Figure 6

The growth-rate function $f(z)$ in the model (4.7).

Figure 7

The future evolution of the growth-rate function $f(t)$ in the model (4.7).